Nadine Dorries won't answer it. Lord Lawson won't answer it. Michael Gove won't answer it. But it's a simple question, and if they don't know it's because they don't want to. Where does the money come from? All are connected to groups whose purpose is to change the direction of public life. None will reveal who funds them.

When she attempted to restrict abortion counselling, Nadine Dorries MP was supported by a group called Right to Know. When other MPs asked her who funds it, she claimed she didn't know. Lord Lawson is chairman of the Global Warming Policy Foundation, which casts doubt on climate science. It demands "openness and transparency" from scientists. Yet he refuses to say who pays, on the grounds that the donors "do not wish to be publicly engaged in controversy". Michael Gove was chairman of Policy Exchange, an influential conservative thinktank. When I asked who funded Policy Exchange when he ran it, his office told me "he doesn't have that information and he won't be able to help you".

Illustration by Daniel Pudles

We know that to understand politics and the peddling of influence we must follow the money. So it's remarkable that the question of who funds the thinktanks has so seldom been asked.

There are dozens of groups in the UK which call themselves free-market or conservative thinktanks, but they have a remarkably consistent agenda. They tend to oppose the laws which protect us from banks and corporations; to demand the privatisation of state assets; to argue that the rich should pay less tax; and to pour scorn on global warming. What the thinktanks call free-market economics looks more like a programme for corporate power.

Some of them have a turnover of several million pounds a year, but in most cases that's about all we know. In the US, groups claiming to be free-market thinktanks have been exposed as sophisticated corporate lobbying outfits, acting in concert to promote the views of the people who fund them. In previous columns, I've shown how such groups, funded by the billionaire Koch brothers, built and directed the Tea Party movement.

The Kochs and the oil company Exxon have also funded a swarm of thinktanks which, by coincidence, all spontaneously decided that manmade climate change is a myth. A study in the journal Environmental Politics found that such groups, funded by economic elites and working through the media, have been "central to the reversal of US support for environmental protection, both domestically and internationally".

Jeff Judson, who has worked for 26 years as a corporate lobbyist in the US, has explained why thinktanks are more effective than other public relations agencies. They are, he says, "the source of many of the ideas and facts that appear in countless editorials, news articles, and syndicated columns". They have "considerable influence and close personal relationships with elected officials". They "support and encourage one another, echo and amplify their messages, and can pull together … coalitions on the most important public policy issues." Crucially, they are "virtually immune to retribution … the identity of donors to thinktanks is protected from involuntary disclosure."

The harder you stare at them, the more they look like lobby groups working for big business without disclosing their interests. Yet the media treats them as independent sources of expertise. The BBC is particularly culpable. Even when the corporate funding of its contributors has been exposed, it still allows them to masquerade as unbiased commentators.

For the sake of democracy, we should know who funds the organisations that call themselves thinktanks. To this end I contacted 15 groups. Eleven of them could be described as free-market or conservative; four as progressive. I asked them all a simple question: "Could you give me the names of your major donors and the amount they contributed in the last financial year?" I gave their answers a score out of five for transparency and accountability.

Three of the groups I contacted – Right to Know, the International Policy Network, and Nurses for Reform – did not answer my calls or emails. Six others refused to give me any useful information. They are the Institute of Economic Affairs, Policy Exchange, the Adam Smith Institute, the TaxPayers' Alliance, the Global Warming Policy Foundation and the Christian Medical Fellowship. They produced similar excuses, mostly concerning the need to protect the privacy of their donors. My view is that if you pay for influence, you should be accountable for it. Nul points.

Civitas scored 1. Its website names a small number of the donors to its schools, but it would not reveal the amount they had given or the identity of anyone else. The only rightwing thinktank that did well was Reform, which sent me a list of its biggest corporate donors: Lloyds (£50k), Novo Nordisk (£48k), Sky (£42k), General Electric (£41k) and Danone (£40k). Reform lists its other corporate sponsors in its annual review, and earns 4 points. If they can do it, why can't the others?

The progressives were more accountable. Among them, Demos did least well. It sent me a list of its sponsors, but refused to reveal how much they gave. It scores 2.5. The Institute for Public Policy Research listed its donors and, after some stumbling, was able to identify the biggest of them: the European Union (a grant of €800,000) and the Esme Fairburn Foundation (£86k). It scores 3.5. The New Economics Foundation sent me a list of all its donors and the amount each gave over the past year, earning 4 points. The biggest funders are the Network for Social Change (£173k), the Department of Health (£124k) and the Aim Foundation (£100k). Compass had already published a full list in its annual report. The biggest source is the Communication Workers' Union, which gave it £78k in 2009. Compass gets 5 out of 5.

The picture we see, with the striking exception of Reform, is of secrecy among the rightwing groups, creating a powerful impression that they have something to hide. Shockingly, this absence of accountability – and the influence-peddling it doubtless obscures – does not affect their charitable status.

The funding of these groups should not be a matter of voluntary disclosure. As someone remarked in February 2010, "secret corporate lobbying, like the expenses scandal, goes to the heart of why people are so fed up with politics … it's time we shone the light of transparency on lobbying in our country and forced our politics to come clean about who is buying power and influence." Who was this leftwing firebrand? One David Cameron.

I charge that the groups which call themselves free-market thinktanks are nothing of the kind. They are public relations agencies, secretly lobbying for the corporations and multimillionaires who finance them. If they wish to refute this claim, they should disclose their funding. Until then, whenever you hear the term free-market thinktank, think of a tank, crushing democracy, driven by big business.

• A fully referenced version of this article can be found on George Monbiot's website