Tony Blair is seen as "out of touch" and "inflexible" by more people than thought the same of Margaret Thatcher, according to an exclusive opinion poll for The Independent on Sunday.

The poll reflects the dramatic change in the Prime Minister's image wrought by his policy towards Iraq, which divided the country at the time of the invasion and continues to do so. It confirms that public opinion is moving against the continued deployment of British troops in Iraq, with a majority wanting them brought home as soon as the Iraqi elections have been held in January.

The poll caps a good week for Charles Kennedy, the Liberal Democrat leader, who stepped up his attack on the Prime Minister's decision to join the invasion of Iraq in his speech in Bournemouth. It gives the Lib Dems a seven-point "conference bounce", lifting them to 27 per cent, only just behind the Conservatives on 30 per cent and Labour on 32 per cent. The poll, part of which was carried out on Thursday, the day of Mr Kennedy's main speech, is a vindication of his claim that "three-party politics" has arrived.

Significantly, the Lib Dems have picked up their extra support equally from Labour and the Conservatives, both of whom have fallen three points since last month. Labour's two-point lead looks slim, but it is in line with the average of other opinion polls carried out over the past six weeks.

And, because of the bias in Labour's favour caused by outdated constituency boundaries, this lead suggests that Labour is on course for a majority of 60-70 at the next election.

The most striking findings in the poll are the dramatic changes in the Prime Minister's image as a result of the invasion of Iraq and its consequences. At the time of the last election, 28 per cent thought he was "out of touch with ordinary people". Now 63 per cent think so - exactly the same number as thought it of Lady Thatcher just before her downfall in 1990. For most of her time as Prime Minister, her score was around 50 per cent.

Three years ago, 11 per cent thought Mr Blair was "too inflexible". Now 57 per cent think so - far more than the 35 per cent who thought the same of Thatcher in September 1990. Despite her fearsome reputation as the Iron Lady, her "inflexibility" rating was around 30 per cent most of the time.

However, it is possible that neither finding is as damaging to Mr Blair as it seems. Few people thought Neil Kinnock was "out of touch" (18 per cent in 1992), but it did him no good, and inflexibility may be a necessary component of being a strong leader.

As well as the double-edged "Thatcherisation" of Mr Blair's image, our poll contains some clearly positive findings for the Prime Minister. Almost half of all voters, 45 per cent, say that he "understands the problems facing Britain", a figure that has risen from 33 per cent at the last election. He is now back to the levels he enjoyed in his honeymoon with the electorate when he first arrived in Downing Street in 1997.

Most surprisingly, perhaps, the numbers saying he is "more honest than most politicians" have also risen, from 25 per cent to 29 per cent. Despite repeated accusations of dishonesty in making the case for military action in Iraq, and the insistent suggestion that the war has fatally undermined trust in him, it seems that a large minority of the electorate has kept faith. Indeed, he fell much further on this score towards the end of his first term, when a mere 16 per cent rated him more honest than most.

Attitudes to the Prime Minister's Iraq policy have, however, shifted significantly against him this year. The IoS poll found a narrow majority of voters, 52 per cent, want British troops to "withdraw from Iraq after the Iraqi elections in January". Opinion remains sharply divided, however, with 43 per cent saying that troops should "stay in Iraq for as long as the Iraqi government wants them".

These figures show a fall in support for Mr Blair's policy of "seeing it through" in Iraq since April, when ICM found that 51 per cent of the public believed that British and American troops should stay for "as long as necessary".

There is a marked gender gap on this issue in our poll, with women supporting withdrawal by 57 per cent to 36 per cent; while most men, 51 per cent, want troops to stay, with 47 per cent in favour of a pull-out.

With Mr Blair's leadership and the ambitions of Gordon Brown, the Chancellor, the hidden story of this week's conference, we also asked how a hand-over of power might affect Labour's standing. The poll suggests that Labour would do better at the next election if Mr Brown were to take over.

Mr Brown as leader increases the proportion saying they would vote Labour by 4 per cent. This would push Labour up to 36 per cent, and double its notional majority to 128 seats. ICM, Mori and YouGov have all reported that a switch to a Brown leadership would increase Labour's lead by 4-6 points, although NOP found a mere 1-point boost last September.

Our poll suggests that one-fifth of Lib Dem voters would switch to Labour if Mr Brown were leader. Fewer numbers would switch from the Conservatives and other parties. The traffic is not all one-way: the poll suggests that Labour would lose some voters to other parties if Mr Blair were to step down. But a Brown leadership would produce a net gain of 4 per cent.

CONFERENCE WEEK: THE INSIDER'S GUIDE

Where to be

Ah, Brighton! Just the place to nip down and enjoy the last of the summer weather, to stroll along the promenade, take a cream tea, and maybe stay over in one of its many hotels, you may be thinking. Well, forget it. There isn't a spare hotel room in the town, or anywhere within a radius of many miles. Traffic will be at a near standstill all week. Crash barriers will be up everywhere, and the town is crawling with armed police in bulletproof jackets. Tony Blair is in town for the annual Labour conference.

Demo of the week

Actually there will be two, one in opposition to the Iraq war, one in defence of fox-hunting. On Wednesday, Sussex Action for Peace will gather at the Peace Statue on Hove Lawns, Brighton, to "raise red-gloved hands skyward in a moving and symbolic protest at their city playing host to bloody Blair and his supporters". On Tuesday, as Blair makes his big conference speech, hunt supporters will rally on the sea front and march towards the conference, with their hounds.

Parties

There are many, many parties and receptions - breakfast, lunch, early evening receptions, late-night bashes, you can party all day if you want. It begins with a party thrown by the New Statesman on Sunday night, and ends with the Daily Mirror held on Wednesday, which features a combo called The Commitments. The smartest printed invitation of the week is the one sent out by the Irish ambassador. Even the Ulster Unionists are throwing a party. Their invitation tantalisingly promises "refreshments" and "a short address by The Rt Hon David Trimble MP". Wild!

For sober people

There are countless fringe meetings, with gripping titles like "Delivering for Communities".

Be seen with

If you want to please the Prime Minister, have a cover of The Goldfish Bowl by Cherie Booth under your arm as you stand chatting to the new election supremo, Alan Milburn.

Don't be seen with

Anyone else who has published a book about Tony Blair this year.

Where will the really, really dedicated be?

Not in Brighton at all, but in Hartlepool, where Labour hopes to hang on to the Commons seat vacated by Peter Mandelson. It will be a bad blow if they lose it, but the news will come too late to affect the mood at conference, because everyone will have dispersed by then.

And Mandelson: gone and forgotten?

No danger of that. Mandelson will be at the conference on Sunday evening, in his new role as EC Commissioner, the star speaker at a meeting with the title "Can we win the referendum on the European constitution, despite the media?"

Andy McSmith