It is not just one or two polls. All recent ones point in the same direction: Gordon Brown and Labour are now in a commanding position, better than he can possibly have dreamt when he became Prime Minister only three months ago.

Of course, Labour’s 41 per cent in this morning’s Populus poll probably reflects some post-conference bounce because it was done on Wednesday and Thursday (among a sample of 948 adults. For more details see www.populus.co.uk).

The four-point Labour gain since the beginning of the month, and five-point drop to 31 per cent for the Tories, compares with the narrowest gap between the parties after David Cameron’s late August counter-attack.

This is, however, the seventh of eight polls this month that have put Labour on at least 39 per cent, and four have been 40 per cent or more. There has been volatility from poll to poll, but the monthly averages have been stable since Mr Brown took over, at about 39 to 40 per cent.

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This compares with 32.5 per cent in May. By contrast, the Tories have been in the 33 to 34 per cent range since the end of June, down from 36.7 per cent in May.

Assuming a uniform national swing, this month’s average implies a Labour majority of well over 100. This compares with a notional 40 or so after taking account of boundary changes, which eliminate about a dozen Labour seats.

Much could change during a campaign as a result of targeting and regional differences: the Tories doing better in the South and the Liberal Democrat MPs holding on against national trends. But the present ratings provide a big cushion against such erosion of support.

Tory advances in some local by-elections on Thursday should be interpreted cautiously because there are not like-for-like comparisons with past contests. There is a patchwork of C-Lab; C-Lib Dem; and Lib Dem-Lab contests in key target seats with the Lib Dems doing well recently.

Moreover, the poll suggests that Mr Brown has a clear edge over Mr Cameron on key leadership attributes: by 59 to 30 per cent on having what it takes to be a good prime minister, and by 60 to 45 per cent on caring about the problems ordinary people face.

In both cases, Mr Brown has improved his position slightly since the first Brown bounce poll in July. Half the public (50 per cent) say that Mr Brown has the answers to the “big problems facing Britain”, against 30 per cent saying that Mr Cameron has.

The only area in which Mr Cameron is competitive is in being “about the future not the past”, where he is rated at 57 per cent, including 51 per cent of Labour voters, against 64 per cent for Mr Brown.

So the Tories’ conference theme of “change” is correct, and they should project Mr Cameron as the voice of the future. In general, however, Labour voters are more enthusiastic about Mr Brown than Tory supporters are about Mr Cameron.

Current polls cannot, of course, predict what opinion will be like next summer or in 2009, when Mr Brown will no longer be so new and economic conditions could be less favourable.

Moreover, while Mr Brown may, probably would, win this autumn, that could be the high point of his premiership and of his authority.

The current drive and unity could be undermined postelection. But that is one risk that Mr Brown may be prepared to take as he contemplates the prize of a fourth term.

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