"Advisers advise, ministers decide." So said Margaret Thatcher when Nigel Lawson resigned as Chancellor in 1989 over the role of Sir Alan Walters, her Downing Street economics adviser. Sir Alan followed soon afterwards.

Similarly, there may be no winners in the increasingly bitter confrontation between the Home Secretary Alan Johnson and Professor David Nutt, who was sacked by email last Friday as chairman of the Advisory Council on the Misuse of Drugs for allegedly "campaigning" against the Government's decision to upgrade cannabis to a Class B drug.

Although Mr Johnson insisted yesterday that the row was an isolated case, it has already become much wider than that. Two other members of the advisory council resigned in protest at Professor Nutt's treatment and others may follow.

The affair also raises questions about the relationship between ministers and their advisers. Ministers admit privately that scientists are worried and will need some "stroking". Mr Johnson will have a lot of reassuring to do when he meets however many members of the council who still remain when it convenes next week.

Ministers insist that Professor Nutt breached the code of practice for advisers by undermining last year's Government U-turn over cannabis, which had been downgraded from Class B to C in 2004. They insist they are not trying to muzzle independent experts but are adamant that the public cannot be given "mixed messages" on such sensitive issues. Ministers argue that the final decision by elected politicians must take account of more than just than scientific advice – such as public opinion, and that Professor Nutt is on the "wrong side" of it on cannabis. They insist that, in this case, the scientific facts are open to dispute, pointing to increasing evidence linking cannabis use to schizophrenia.

Yet many scientists are alarmed, accusing the politicians of wanting to have their cake and eat it – parading and citing experts when they agree with their policy and silencing or even dismissing them when they disagree. They point out that Professor Nutt was not a civil servant but an expert academic who was not paid for his work on the council. In effect, they accuse the Government of preventing him from doing his day job.

Ministers may have unwittingly bitten off more than they can chew. At a time when trust in politicians is at a low ebb after the MPs' expenses affair, independent advisers play a vital role in reassuring the public and communicating with them in a crisis. Witness the sure-footed performance of Sir Liam Donaldson, the chief medical officer, on swine flu. (Ministers point out that he accepted the Government's decision to reject his proposal for alcohol to be priced according to its strength and did not campaign against it as Professor Nutt did on cannabis.)

Some scientists are worried that the Nutt sacking turns on its head the relationship between advisers and ministers. The last Tory government suppressed and rejected scientific advice that mad cow disease could spread from cattle to humans because it conflicted with its policy that British beef was safe. It later accepted that it should have listened more carefully to the experts. The official inquiry into the BSE crisis concluded that "scientific investigation of risk should be open and transparent" and that "the advice and the reasoning of advisory committees should be made public". Without such openness, it warned, people would not believe a government.

The weakness in the Government's argument on cannabis is that it was an open secret it had already made its mind up before it received the council's views. One of Mr Brown's first acts on becoming Prime Minister in 2007 was to announce a review of the classification of the drug, pointing to public concern about the growing use of stronger skunk. It was his "not-Blair" phase as he sought to appeal to Middle England; he also announced a review of 24-hour drinking and killed off his predecessor's plan for a super-casino. So it was no surprise when the advisory council's proposal for cannabis to remain in Class C was rejected by the then Home Secretary, Jacqui Smith, last year.

His critics claim Mr Brown has form. As Chancellor, he set up several "independent reviews" by outside experts which – surprise, surprise – normally recommended exactly what he wanted to hear. The most important was by the former banker Derek Wanless, whose review of the NHS gave Mr Brown cover for a landmark 2002 rise in national insurance to boost health spending.

Things didn't always go according to plan, and some advisers are more independent than others. Mr Brown hit the roof over the cost of Lord Turner of Ecchinswell's recommendations on pensions, but Mr Blair ensured the bulk of his review was implemented.

Nor has Mr Brown's attempt to bring in outside experts as ministers proved an unalloyed success. Most of his "goats" (short for "government of all the talents") reached the end of their tether rather quickly. Lord Malloch-Brown, Lord Darzi, Lord Carter, Lord Jones have come and gone, the latter describing his spell as Trade minister as "dehumanising and depersonalising". Despite that, David Cameron is looking at ways of bringing businessmen into Whitehall and possibly into his government.

There may be far-reaching implications from the Nutt affair. Prominent scientists sense an opportunity in the crisis and are drawing up a code of practice for both advisers and government. Ministers would recognise that advisers should enjoy academic freedom, seriously consider all expert advice and, if they rejected it, publish the original recommendations and their reasons for saying "No".

Evan Harris, science spokesman for the Liberal Democrats, said: "If he [Professor Nutt] can't express an independent view, he is dependent on the Government. The whole point of having scientific advice is that [scientists] give it without fear or favour. If they only give advice that ministers will agree with, [the Government] is not getting good advice."