Gordon Brown has bounced. The search for a "Brown bounce" has been going on for some time, but until the early hours of yesterday morning the results were inconclusive. After Labour's victory at the Glenrothes by-election, Brown can claim with justification to be moving upwards. He is back in the political game, a remarkable turnaround from his position two months ago when some within his party assumed and hoped that a defeat in Glenrothes would be the final nail in his coffin.

I had concluded that Labour would not win another by-election anywhere up to the next general election. Angry voters would give the Government a kicking and that would be more or less the end of the matter. In Glenrothes they did the opposite, returning to the fold in larger numbers than even the most optimist Labour figure had dared to predict in advance.

There are, of course, distinctive features of the by-election that cannot be applied to the national picture. In this case, the SNP is the incumbent administration in Scotland, enabling Labour to campaign almost as the opposition. It will not be able to do that in the rest of the country at a general election. Arguably Labour supporters are more instinctively tribal in Scotland than in parts of England, not least in Glenrothes, a constituency that borders Brown's. In Scotland, the Conservatives are nowhere to be seen. In England, David Cameron has made more waves. There is no guarantee that Brown will bounce when middle England gives its verdict at a general election.

Nonetheless, even considering the result in this more limited context, there are some highly significant pointers. The by-election result means the SNP honeymoon in Scotland is over. Since Alex Salmond became First Minister in 2007, he has enjoyed an almost uncritical adulation. He will be subjected to more intense scrutiny from now on. More widely during the summer it looked as if Labour's brand was in danger of becoming fatally contaminated when it was slaughtered in the by-election in Glasgow East last July, one of the party's safest seats. The result in Glenrothes suggests that at the very least Labour has an audience again.

Above all the by-election is a testament to Brown's wilful political stamina. People are always writing him off. He always bounces back. In terms of his wildly oscillating relationship with the media and the public, he is the Bruce Forsyth of British politics. I have followed both careers closely and the two of them have an almost unique capacity to keep going in adversity on the assumption they will rise again.

Forsyth was written off by critics after being the star of Sunday Night at the London Palladium. He returned triumphantly with The Generation Game. His subsequent switch to ITV was a disastrous flop. That was supposed to be the end. He bounced back with Strictly Come Dancing. Each time the critics hailed him without acknowledging they had written him off on several previous occasions.

Brown is Bruce without the jokes. Here is a brief summary of the Prime Minister's relationship with the voters and the media. In 1992, he was the star of the Labour Party and widely seen as a future leader. In 1994, he was so unpopular that Tony Blair became leader instead and Brown's soaring ambition seemed doomed. By 1998, he was seen as a triumphantly dominant, popular and widely respected Chancellor.

In 2001 he was written off as a marginal figure as Blair became a global leader after 11 September. After his 2003 Budget he was hailed as a great reforming Chancellor. By 2004, he was a marginal figure once more, not even invited to cabinet meetings that planned the next election. In 2005, he was so popular that Blair had to affect a rapprochement and bring him back to the heart of the general election campaign.

In 2006, he was so unpopular that polls suggested Labour would fall further behind if he became Prime Minister. When he became Prime Minister, he was so popular he was tempted to call an early election. After deciding not to do so, he became the most unpopular prime minister in history. Now he breathes again.

I write that summary not to suggest that Brown is on course to win the next election. It would be absurd to draw such a conclusion from a single by-election. But given that in September the main political conversation was over who would replace him, this autumn he has already staged another comeback. That is the limit of it so far. He has reached a position where it is almost certain he will lead Labour into the next election.

The missing element to a more spectacular recovery is a lead in the national opinion polls. Brown's bounce is not the equivalent of a spectacular trampoline leap. So far, most polls suggest that the Conservatives' lead has fallen but that Cameron's party is still ahead by a commanding margin. If that were to change in the coming months, a general election next year becomes probable.

It is, of course, a big "if". Ministers still fear that when the recession deepens, Labour will become more unpopular rather than less. But some of Brown's allies are suggesting discreetly that if he continues to bounce upwards he should call an election next year and avoid the nightmare of staggering on until the last possible moment. Only yesterday one of them put a powerful case to me for Brown calling an election in the autumn of next year. A Blairite who used to work in Downing Street predicts that Labour will be ahead in the polls by early next year and that Brown will and should call a spring election.

All that can be said for now is that such tentative election speculation reflects a changed political situation. Before Labour's conference in September, the only election that seemed possible was one for the party's leadership. Brown faces many dangers in the midst of what might be a deep recession, but he should never be written off.