Most children aged eight to 11 are shopping online, buying apps and have bank accounts, yet may receive no financial education at school.

So says the Personal Finance Education Group (PFEG) which is urging that primary schools should follow secondary schools south of the Border and introduce formal money lessons.

In Scotland, the Curriculum for Excellence already includes financial education, though it is not compulsory and coverage is patchy, relying on teacher enthusiasm and outside support.

The last survey by the Scottish Government four years ago found 14% of P1 pupils getting some financial education, rising to 41% in P6 then dipping to 38% in P7 - still well under half.

The survey by PFEG and the British Bankers' Association found 64% of children get their first bank or building society account before they start secondary school, 63% already have a mobile phone, 58% have bought something or had something bought for them online, 74% have access to a tablet and 57% of those have downloaded a paid-for app, on their own or with help, onto their tablet or smartphone.

"Despite this, children have a worrying lack of knowledge about banking and personal finance," says PFEG. Only 23% of eight to 15-year-olds had heard of a current account and understood how it worked and only 13% were aware of overdrafts.

Tracey Bleakley, chief executive of PFEG, says: "We know from experience that the earlier financial education starts, the more effective it is in giving young people the skills, knowledge and confidence they need to manage their money well."

The survey found 49% of children had a bank or building society account in their name before the age of eight. Among eight to 15-year-olds, more than one-third had a cash card, 49% used it at least once a month, and 11% already used online banking. Three-quarters of 15-year-olds had a debit card.

Step forward parents, who start doling out pocket money from an early age and can play a key role in early money sense.

The latest Aviva Family Finances report reveals that three-quarters of parents in Scotland provide pocket money, paying on average £3.83 a week (ages five to eight) and £4.62 (ages nine to 11). Five is the typical age for a child's first savings account, with 37% of youngsters up to age 15 having some savings.

More than one-third (38%) of parents said that they chose their child's bank or building society, and the type of savings account opened.

"However, control over their child's money often stops there, as 45% of parents admit to letting their child spend their pocket money on 'whatever they like' each week," says PFEG.

But one-third tried to encourage some sort of savings habit from a young age, with 21% inspiring them to save something for a "rainy day". A further 9% go a step further and encourage them to save some pocket money for the long term.

Tim Orton at Aviva says: "Although many parents continue to pay pocket money indefinitely, or as long as their child needs it, there are encouraging signs that some do try to persuade their teenagers to get a part-time job in order to provide them with some financial independence and future security."

Orton continues: "Teaching children how to manage their money from an early age and save something is an important trait. Saving a little and often will stand them in good stead for later life."