Gordon Brown's attempt to relaunch his government has flopped, according to a poll for The Sunday Times, and his unpopularity is on a par with the worst days of John Major.

With last week’s £2.7 billion tax cut and a raft of new measures in the draft Queen’s speech Brown hoped to improve his standing but the survey of more than 1,800 people by YouGov gives David Cameron’s Conservatives a 20-point lead over Labour, up four points on last month. It suggests the Tories are establishing commanding leads of the kind enjoyed by Tony Blair before Labour’s 1997 landslide.

The Tories had 45% of the poll, up one on last month, with Labour on just 25%, down three, and the Liberal Democrats on 18%, up one. If repeated at a general election, this pattern would give Cameron more than 400 seats in the House of Commons and a majority of about 150 over all other parties.

The poll is a blow for Brown before this week’s by-election in Crewe & Nantwich. If the swing from Labour to the Tories shown in the poll were repeated in the Cheshire constituency, the Conservatives would make their first by-election gain from Labour for 30 years.

Even more troubling for the prime minister is the continued slump in his personal poll ratings. Last month YouGov showed Brown had suffered the sharpest drop in ratings of any modern prime minister — worse even than Neville Chamberlain in 1940.

This month’s poll shows only 17% think he is doing well while 78% say he is doing badly, a negative rating of 61 points. This is close to Major’s nadir of -63 points in January 1995. Cameron, in contrast, is enjoying his best positive rating, of 33 points.

By three to one, 69% to 21%, people say Brown is not up to the job of prime minister, showing that even some Labour supporters have serious doubts about his abilities. Only 8% think he can lead Labour to victory in the next general election.

Brown is suffering the effects of a number of recent botched moves. By 47% to 23%, voters thought last week’s decision to head off the rebellion over the abolition of the 10p tax band by raising personal allowances was a reflection of the government’s weakness, not its strength.

More people said Brown’s actions made them less likely to vote Labour than said they had renewed confidence in him.

Labour’s problems appear to be mainly down to the state of the economy. After the Bank of England governor’s warning last week that the “nice decade” is over, 60% of people think that house prices will fall over the next year and a similar proportion think the economy will not grow or will head into recession.

People say they are spending less on clothes, eating out and other non-essentials and are checking supermarket prices more often. More than nine in 10 say they are “ripped off” by energy companies.

The government is also getting the blame for the economy’s woes. Brown said last week he was the man to steer the economy through the crisis but two-thirds of people, 65%, blame him at least in part for the problems. The long lead that Labour enjoyed on “competence” — whom voters most trust to run the economy — has disappeared.

Cameron and George Osborne, the shadow chancellor, are now ahead by two to one over Brown and Alistair Darling, the chancellor.

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