I WAS born in 1936 into a polarised Britain.

My paternal grandfather was the son of a village blacksmith, who moved to the town of Barking, south-east London, to look for a job. He struggled to find steady employment, however, and only escaped the workhouse when his kindly landlady let his family stay on without paying rent. Eventually he became a bricklayer at Barking railway station, but he was knocked over by a train. His leg was amputated and, lacking adequate medical care, he died in the rooms where my family lived, a week before I was born.

My father also experienced unemployment but later found work as a roofer in Brighton, earning the cash to feed mum, my older sister and me. He managed to buy and repair an old van and turned himself into a removal man. With a better income, he moved the family to a semi-detached house on a busy road in Ilford. Meanwhile, the rich lived in luxury and ease. My father knew something about this as he sometimes moved them. He complained that "the posh" never gave a good tip, but he was careful always to call them "Sir" and "Madam".

Ilford, with its large munitions factory and nearby docks, was heavily bombed during the war. One evening, my father had been working late as an air-raid precaution – ARP – warden. When the air-raid siren went, he was slow getting out of bed for the usual dash to the shelter. As we stood on the landing, we heard bombs exploding, a German bomber flying low ... then a spray of bullets came through our window. The plane had been hit and was firing its machine guns as it plunged to crash. A narrow escape.

Out shopping one day, I was in the greengrocer's when I spotted a doodlebug: one of the Germans' dynamite-packed pilotless planes which acted as flying bombs. I froze ... then someone dragged me under the counter as the front of the shop blew in. The explosion destroyed the terraced houses just 50 yards away, and some of my neighbours died, but again I was safe.

At that time, I rarely went to school because mum wanted me with her so we could rush together into our air-raid shelter. But then came the V2 rockets. Faster than sound, they arrived without warning so there was no chance of taking shelter, and mum decided my sister and I might as well go to school. Besides, she now had a new baby.

On my baby brother's first birthday, the school was rocked by a tremendous explosion. A V2. We were sent home to a scene of destruction: lorries strewn across the road, bodies in the street. I walked into what was left of our house. I knew my sister was at school, but what about mum and the baby? Then dad appeared and told me they had been dug out by the ARP. They were in hospital, injured but alive. We were promptly evacuated.

In 1945, war over, I returned home and was sent to the local junior school. I was deemed backward, and at the end of the year I failed the 11-plus exam: no surprise to my teachers and no worry to myself or my parents. But I failed so badly that I was kept at junior school for an extra year and so separated from all my mates. I was a blitz scarred-child – terrified of death yet unable to speak about it, scarcely able to read, and struggling to learn sums. I had good parents, but they did not have educational ambitions for me.

So how was it that I later made it to grammar school and university, and eventually became a university professor? The answers may prove useful today as we try to help socially disadvantaged children whose abilities do not blossom.

I had an inspiring teacher at junior school. She must have spotted something in me and her words still ring in my ears: "You can do it, Robert." She gave me attention and homework. She asked what was my favourite radio programme and, when I replied, Just William, she handed me an exercise book and said: "Write a play about him". I toiled over it and then she got the class to perform it. At the close, they applauded and so did a beaming teacher. For the first time, I was receiving praise for school work.

I took the 11-plus again and guess what? I failed. But a local secondary modern school was being upgraded to grammar, and offered to take on the top 60 who had failed the exam. I was one of them.

As the only boy from our neighbourhood to get in, I struggled at grammar school. Lining up in the playground on the first day, I received a clip round the ear for speaking to the boy next to me. I had been trying to make a friend. I did chum up with another lonely boy, who told me about a local youth-club football team. I asked if I could join and he said I'd have to attend its Sunday meeting. It turned out to be a Christian voluntary club led by two men who had a great influence on me. They lent me books and persuaded me to take school seriously and improve my behaviour.

I did well at O-level exams and teachers urged me to stay on for A-levels and university. The club leaders said the same. Trouble was that my parents – good, loving, working-class people – wanted me to get a job. Dad handed me application forms for a post as a town-hall clerk. "You'll never be unemployed and you'll get a pension," he said. I filled it in. Then one day dad came into my school to remove some furniture, and two teachers convinced him of the advantages of letting me stay on.

The Family Allowances Act of 1945 meant a lot to my family. The precursor to today's child benefit, it provided five shillings (25p) a week for second and subsequent children, until they left school. So I stayed in education and, when I won a state scholarship to London University, mum and dad were proud of me.

After graduating, I joined one of the growing number of local authority children's departments before being recruited as a university teacher. I would go on to become professor of social policy at the University of Bath. I was socially mobile at a time of nearly full employment in a less polarised Britain. The 1950s to the 1990s was a period of social improvement and the numbers gaining school qualifications and higher education grew.

Today, by contrast, the outlook is bleak for many youngsters in the lower reaches of society. The social rights campaigner, Desmond Tutu, talked recently of "the growing gap between rich and poor, between the powerful and the powerless, between those with unfettered dreams and hopes and those focused on mere survival". He was talking about Britain.

Our society is divided into socially deprived areas and what some social scientists call "gated communities". Although the latter term originally described places where rich residents literally kept inferiors out with gates and railings, today it means neighbourhoods inhabited by people with high salaries, two cars and perhaps even second homes. Good shops and leisure facilities abound, and the well-resourced schools achieve excellent exam results and high numbers going on to universities.

Socially deprived areas, meanwhile, are characterised by high levels of poverty, unemployment, low car ownership, inadequate leisure facilities and sometimes long-established gangs. Their schools often have good teachers but, given the proportion of socially disadvantaged youngsters, they struggle to give the individual attention I received as a child.

In Britain today, poverty is higher than ever. The number of families in bed-and-breakfast accommodation has grown sharply and in the last five years, food prices have risen by 32%.

Food parcels have returned and doctors have urged the Government to provide free school breakfasts. The millionaire ministers say this is impossible at a time of austerity. Meanwhile, Work and Pensions Secretary Iain Duncan Smith, who has announced plans to change the way that child poverty is measured, also wants to restrict child benefits for families with more than two children. This, in a Britain where 2.5 million people have second homes. The polarisation of my childhood is back.

What can be done to promote the academic and job prospects of disadvantaged young people? The Nobel Prize-winning economist Joseph Stiglitz makes clear that the answer is greater material and social equality. This confirms the study by Richard Wilkinson and Kate Pickett whose book, The Spirit Level, demonstrated that countries with the least social inequality perform best at every level, including educational attainment. In countries such as Norway and Finland, social mobility is higher and unemployment lower; the welfare state continues and a sense of community rather than division prevails.

Unfortunately, in Britain, no major political party is seriously committed to promoting greater equality. Their leaders talk vaguely about it but offer no specifics about the redistribution of income – let alone wealth. We should persuade our parties to be serious about equality. We can also attempt to do something in our own occupational and social spheres.

In 1976, I left my job as a university professor and moved with my wife, Annette, and our family to the Southdown council estate in Bath, to set up a project for local young people. Eleven years later, we moved to Glasgow's Easterhouse and joined with local residents in forming Family Action in Rogerfield and Easterhouse (FARE). Operated from one small room, with myself as part-time leader, it had something in common with the youth club which helped me in my childhood.

When Duncan Smith, then Conservative Party leader, visited Easterhouse 10 years ago, he was amazed at the abilities of volunteers who were unemployed or single parents. He said Maggie Thatcher used to criticise these people. When he spotted a drug-user's discarded needle in the gutter, he was distraught. As a wealthy, privately educated former army officer, he'd had no idea of what life was like in deprived places. He was also surprised to learn that Annette and I had sent our own children to Southdown's nearest state comprehensives. He seemed to feel that we had sacrificed them. But teachers in deprived areas don't lack ability and drive, and both our children went on to university (our daughter is now a medical doctor and our son is a senior lecturer in psychology).

Living in Southdown also meant that we could lend our support to one of its schools. This kind of support is taken for granted by schools in affluent areas, whose pupils are also more likely to gain contact with educationally and professionally well-connected people. Research by the educationalist Stephen Gorard shows many working-class children are as intelligent as their middle-class peers but are less likely to get into universities and top jobs because they lack the right contacts.

Today in Easterhouse, FARE is working hard to improve access to educational opportunities. Led by Rosemary Dickson, it draws in 500 children a week to its purpose-built headquarters. Its youth clubs and holidays provide positive experiences of the kind from which I benefited, and there is a room of computers, space for homework, and staff who take an interest in the children's education. There is support for children struggling to make the transition from primary to secondary education, and the organisation works closely with local schools to help counteract the influence of gangs. Significantly, violence and vandalism have dropped in the area, and children are less likely to take on the gang attitude that school and study are not cool.

FARE co-operates with six secondary schools in Glasgow's east end, in order to enhance the futures of youngsters likely to become "Neets" (not in education, employment or training). Of 180 participants who left school in 2011, 162 went on to jobs, further education or training.

Stef Hughes, who lived close to me in Easterhouse, was one of the first to join our clubs. Brought up by a hard-working lone mother, he went to a local secondary school and gained a few standard grades. He had talent but, he says: "I never applied myself", and he left with no Highers. He worked in McDonald's, in pubs, as a bus driver. None of these jobs satisfied him because, he says, FARE planted "a sense of responsibility for others in me". He became a volunteer club worker at FARE. Encouraged by the leader, he went to college and gained qualifications in social care and computing. His breakthrough came with a post in residential childcare and then as a mentor with the Unemployment League in Glasgow. His ability was recognised when he was appointed operations manager of a new league in Manchester.

Stef has benefited from a good mum, teachers who valued him, and a local project. He has been encouraged, advised and praised. Just like me. He is now 36, married with a daughter. We still keep in touch. Three years ago I had cancer. Stef came to see me. He told me that FARE had kept him out of trouble and showed him the kind of work he could do. He also encouraged me and taught me about his new work. Now we are not youth leader and club member, we are friends.

Local projects cannot abolish polarisation. They can modify its effects in a few areas. They do show that change is possible. But even this is under threat. FARE's grants, like those of many voluntary bodies, are being cut. As an academic and a local activist, I believe widespread educational improvement requires a more equal society. My view on Scottish independence will be shaped by whether or not it will promote that end.

Bob Holman is the author of Keir Hardie: Labour's Greatest Hero? (Lion Hudson, £10.99). He will be discussing the educational needs of marginalised children at a Pupil Inclusion Network Scotland seminar in Glasgow on November 29. www.pinscotland.org