The ministers wanted to go far further than Virginia Bottomley, Secretary of State for Health. Despite such heavyweight backing she has failed to deliver such a ban, and has told Cabinet it is not justified.
Mr Heseltine's call for an 'outright ban' came in response to proposals last November from Mrs Bottomley for only limited further restrictions on advertising.
He was supported by John Gummer, Secretary of State for the Environment, while William Waldegrave, Chancellor of the Duchy of Lancaster, also favoured such a move.
Mr Heseltine said he found Mrs Bottomley's stance 'surprising . . . given that the Department of Health's review said that further restrictions, including a ban, would reduce smoking and thus save lives'. He added: 'An outright ban instead of some halfway house of severely constrained advertising is the credible way forward.'
Mr Gummer told John Major he fully supported Mr Heseltine's line. 'If the Government want to be seen to be serious about reducing the prevalence of smoking and improving people's health, the right course of action would be to go for an outright ban on tobacco advertising.'
Mr Waldegrave supported Mrs Bottomley's recommendations but raised the possibility of a ban by saying he would not have opposed one 'if Virginia had felt able to move that far'. The principle of a ban was agreed 'years ago' when cigarette commercials were banned from television.
Next week health ministers will announce new restrictions on advertising, but it is understood that these will not even meet all Mrs Bottomley's November recommendations to the Cabinet.
Ministers hope enough will have been done to head off a Private Member's Bill from Kevin Barron MP. His Tobacco Advertising Bill, in favour of a total ban, has its Second Reading on 11 February.
Mrs Bottomley warned her colleagues in November that it was not clear that the Government could ensure a majority against such a move. 'Current policy is vulnerable in Parliament,' she said.
Evidence from Canada, New Zealand, Norway and Finland, where tobacco advertising is illegal, is that it can cut smoking by about 6 per cent. Other estimates accepted by Mrs Bottomley and quoted in her memo to Mr Major say that each 1 per cent reduction in smoking could be expected to save 1,100 deaths a year in the longer term.
David Pollock, director of Action for Smoking and Health, said: 'Mrs Bottomley plainly believes that a ban could save thousands of lives.'
Her memo says stricter advertising controls 'could be expected to reduce smoking', but she adds: 'In my view, the evidence available does not provide sufficient justification for imposing a statutory ban on all forms of tobacco advertising.'
She recommended instead a new scheme to limit the tax breaks for the tobacco industry, and sought to further restrict children's exposure to advertising material, probably by banning advertising on hoardings and shop fronts.