The poll shows overwhelming dissatisfaction with Mr Major among ordinary voters. Fewer than one in five (18 per cent) think he is doing 'very' or 'fairly' well as Prime Minister; 62 per cent say he is doing very or fairly badly.
Asked to choose which of seven leading Conservative politicians would be 'the best Conservative Prime Minister for the country at the moment', Mr Major is nominated by a mere 12 per cent, putting him in a humiliating fourth place behind Margaret Thatcher (18 per cent), Michael Heseltine (14) and Kenneth Clarke (13).
Fifty-six per cent of voters think Norman Lamont was right to criticise him in the Commons and only 27 per cent think that Conservative MPs should encourage him to carry on until the next election. The blunt message is that Mr Major is a bad Prime Minister who ought to quit.
What will particularly disturb Conservative party managers is Mr Major's plummeting stock among true-blue supporters. Only 27 per cent of all voters say they will stick to the Conservatives at the next election. Even among loyalists barely one in three regard him as fit to be Prime Minister and only 36 per cent could bring themselves to say that he was doing 'very' or 'fairly' well.
Only 29 per cent of Conservative voters could be mustered in Mr Major's support when asked which of seven Conservative politicians would now make the best Prime Minister. Just as many plumped for Lady Thatcher.
The power of the Thatcher legend is even more apparent when voters are asked about their preferred successor to Mr Major. She emerges as one of three equal frontrunners, alongside Michael Heseltine, her former challenger, and Kenneth Clarke, Major's likely challenger. Among loyalists - who intend to vote Conservative next time despite everything - she is the firm favourite, though a comeback would be constitutionally almost impossible, now that she is a peer.
Despite Mr Heseltine's unpopular decision last November to shut down 31 coal mines, voters favouring the opposition parties fractionally prefer him to any other Conservative. As it is among current Labour and Liberal Democrat supporters that the Conservatives must make converts to win the next election, some Tory MPs may be persuaded that Mr Heseltine's career is not over.
The poll makes more cheerful reading for opposition leaders. Ordinary Labour voters do not echo the murmurs of doubt about John Smith's leadership among some Labour MPs, activists and union leaders.
Fully 68 per cent of Labour voters are confident he would do well as Prime Minister and only 8 per cent believe he would do badly. Asked to choose which of seven Labour politicians would make the best leader of a Labour government, John Smith is the runaway winner (48 per cent) and the young pretenders - Margaret Beckett, Tony Blair, Gordon Brown, Robin Cook and John Prescott - are all also-rans.
The fly in Labour's ointment is that its vote, at 42 per cent, has drifted down from the high 40s of the late autumn and winter. The Liberal Democrats' revival has been primarily at the Conservatives' expense but it has dented the Labour vote too.
Paddy Ashdown emerges as the most respected of all three leaders, with a positive net rating of +15 per cent compared with John Smith's +11 per cent and John Major's negative rating of -44 per cent. Given his limited exposure in the media these figures may reflect voters' scepticism about Smith and Major more than their faith in Ashdown.
The figures do contain some pinpoints of light for Mr Major. Most of those who voted Conservative in 1992 - and must do so again if the party is to win next time - have suspended final judgement. Only 24 per cent think the Tories should get him to resign; the remainder think the party should give him another year (32 per cent) or soldier on under his leadership until the election (42 per cent).
This suggests that the electoral test for Mr Major will not be the Christchurch by-election, but the local and Euro-elections next summer. The Tories did very badly when they were last held, in 1990 and 1989 respectively. If the economic recovery is enough to enable the Tories to make modest gains he may well be saved; if not, a leadership challenge in autumn 1994 seems inevitable.
Ivor Crewe is Professor of Government at the University of Essex.
NOP interviewed a representative quota sample of 1,094 adults in 54 constituencies across Great Britain on Friday 11 June.