THERE is no shortage of charity in Britain. You realise as much when Comic Relief celebrates raising £1 billion in three decades, when wars destroy lives, or when natural disasters strike. The British give and they give freely.

You can attach rough numbers to the instinct. The Office of the Scottish Charity Register estimates that its sector “handles” over £10 billion a year. According to the Charity Commission, the income generated in England and Wales is £64.2 billion. That's a lot of charity. Set it beside a Ministry of Defence budget of £38 billion and it might even ease a few consciences.

Charity remains an odd affair, for all that. Most of us could name plenty of good causes. Could we nominate 23,910? That's the figure for regulated “community groups, religious charities, schools, universities, grant-giving charities, and major care providers” in Scotland. The statistic for England and Wales is still more astonishing: 164,161 “main charities” operate, together with 16,705 subsidiary bodies. Around a million jobs are involved.

The third sector is an industry, then, and a big one. There is a lot of duplicated effort – over 250 animal charities, close to 600 fighting cancer, almost 2,000 working with and for children – and no shortage of controversy. Kids Company and its founder, Camila Batmanghelidjh, have captured their share over the last few days. Arguments over culpability aside, the organisation's collapse has raised serious questions about the nature and role of charities.

Once they did jobs that Government could not or would not do. Now the Cabinet Office, local authorities and other charities are struggling to cope with a reported 6,000 vulnerable children for whom Kids Company had been allowed to take responsibility. Not only had Batmanghelidjh's organisation supplanted official providers of care, it was dealing – so she says – with youngsters who were referred to the charity by councils.

This was what David Cameron used to call his big society: a private social enterprise as a substitute for the state. For long enough, the Prime Minister – personally, it seems – backed this effort with public money. Over the course of a decade, 2005 to 2015, the Kids Company received around £37 million in Government grants. Now, seemingly overwhelmed by financial problems, it shuts its doors. Would even the worst council social work department have been allowed to get into that position, or respond in that manner?

According to an analysis published by the Centre for Policy Studies (CPS) in January, the top 50 charities in England and Wales by revenue accounted for 21% of all “charitable resources” last year. Of that, fully £3.1 billion was public money. In other words, 24% of the top 50's “incoming resources”, excluding various tax exemptions, came from the public purse. One question is simple: why should services be funded in this manner? A second question involves the effects on the charities.

Kids Company collapsed, remember, when the Government tried to claw back £3 million within a matter of weeks and a reported philanthropic donation for another £3 million failed to materialise. The charity was providing a public service without the controls, financial or political, you would expect in a Government department. The human cost is now becoming evident. The episode is not a judgement on 200,000 or so other organisations in the charity sector, of course, but it illustrates the risks being run by some.

What becomes of their independence from government? Who exercises public responsibility for public money? Where's the transparency and where does the buck stop when things go wrong? In essence, Batmanghelidjh was operating her own quango, dependent on the taxpayer, with her own direct line to the Prime Minister. But which legitimate arm of any government simply pulls down the shutters in a crisis?

The word “charity” is probably too vague to be useful. You cannot easily compare the noble Donkey Sanctuary with Oxfam. Last year the former raised a remarkable £32.4 million, mostly from legacies. In 2013, the latter had an income of £367.9 million, 5,000 employees, and a potent political influence. But Oxfam was also in receipt of £38.26 million in Government money, mostly in the form of international development grants.

You could not accuse the charity of curbing its tongue as a consequence. Equally, you could ask if such a situation is healthy for an international aid organisation operating in places where the UK Government is not popular. What follows, in any case, when charities come to depend on Government contracts for income?

Kids Company provides one example. Perhaps, to be fair, it counts as an extreme case. But how easily do bigger, better-established organisations speak out on issues that matter when a minister or a council official is signing the cheques? The CPS noted, for example, that the likes of Age UK, Action for Children, Royal Mencap and Barnardos are all heavily dependent on public contracts. Are they still, in the real sense, charities?

Yes and no. In one guise the biggest among them are corporate organisations with the full panoply of chief executives, finance directors and the like. There are salaries to match. Someone at Marie Stopes International, the family planning charity that gets £21 million (12% of its income) from the Government, earned better than £290,000 last year. The author David Craig, a stern critic of the sector, states that 17 employees of the six biggest anti-poverty charities each earn more than £100,000.

The same organisations bombard the rest of us with heart-rending TV ads. They hire people to call us at home – incessantly, by some accounts – or stop us in the street in their search for cash. Is this an appeal to charity in the purest sense? Is it harassment, a demand for alms, or unpleasant and offensive “chugging” (charity mugging)? Martin Sime, chief executive of the Scottish Council for Voluntary Organisations, has just demanded the resignation of William Shawcross, chair of the Charity Commission, for criticisms of such commercial fundraising.

Sime, like many charities, thinks Shawcross is endorsing a caricature. My recent experience – a UN appeal for Syrian refugees, no less – says the depiction is not so far from the truth. When giving ceases to feel to a voluntary act, those soliciting donations have a problem. The case of 92-year-old Olive Cooke, found dead in Avon Gorge in May after allegedly being inundated with charity appeals, might be unrepresentative. Nevertheless, compassion fatigue is a cliché born of uncomfortable truths.

It also contains the paradox of charity. Cameron and his kind seem to harbour the belief that much of society's needs could be met by the enterprise of people like Batmanghelidjh and compassionate giving. Charity and philanthropy, they imagine, could render the intrusive state redundant. If thousands of vulnerable children can be left to depend on the efforts of Kids Company, why not other aspects of public responsibility? Or does the idea of being pestered in the street for a few bob to keep the NHS alive reveal a tiny flaw in that fantasy?

If things matter to a society, they should count as social and political priorities, paid for openly from the public purse. Chuggers and charismatic entrepreneurs in compassion do more harm than good.