Mr Cameron has expressed frustration at Mr Brown's stance

Here is a selection of comments from observers interviewed by the BBC.

The weakness of Brown's position is that he allowed speculation to grow over the summer months.

That's done him damage because it looks weak and indecisive, and however good a face he tried to put on it this morning, he's bottled it, to use that dreadful word.

I think David Cameron comes out of this indisputably well. Gordon Brown blinked first.

Cameron's own right wing was muttering into its chin in Blackpool last week, saying 'we'd better keep quiet, there's an election coming'. He'll be able to face them down much more easily.

Brown has got something out of it, he's forced the Tory tax plans out of their box prematurely, but it's not much.

In my view this was a completely unforced error. I didn't think there was a particularly strong case for a snap election.

I think it was dreamt up as a wheeze with which to unsettle the Conservatives over the summer.

The Conservatives were having a dreadful summer, and Brown thought it would be fun to make them rather more miserable.

I think it achieved that aim initially, but what started off as a wheeze became a serious idea.

The question is, can the Conservatives make this a big issue? Can they present Brown as the bottler, the man who won't let you have a vote on the referendum? Can they make that stick?

I think the challenge for Cameron now is to keep the momentum up. I mean, he now faces perhaps two years or more before the election - it's pretty clear there isn't going to be an election in 2008 - so he has to keep this initiative going.

That's a further test of his leadership. He's moved into a different phase now.

I mean, we've had a period over the summer where many people were writing him off. He's now got a chance, he's got to build on that.

I think it is a disaster because it goes against the image that Gordon Brown has set himself up as a solid, unflappable person who has been through, after all, bombs and floods and pestilence and all the rest of it, and all of a sudden it's he himself who's knocked himself out.

But on the other hand, a week is a long time in politics. I bet if you asked us back in a couple of weeks we'll be talking about something utterly different.

It will disappear very quickly, it will remain as a sort of blip on the landscape.

But I think it does change the way Brown has to be from now on. I don't think he can simply sit there being rather pompous and rather solid and terribly reliable.

He's got to actually be a bit insurgent. I think he's got to start for the first time, which he didn't in his party conference speech, making a case for Labour.

We have a three-point Conservative lead, they are at 41%. That's the highest figure the Conservatives have been at for 15 years, since before Black Wednesday in 1992.

It's been a massive turnaround. We had the Conservatives at just 32% just 10 days ago - a nine-point jump.

I can't remember something like that happening since the Falklands War 25 years ago.

[But] at the moment the public, or a large number of voters, are not fixed in their views.

So Labour has a good week, Labour shoots up. The Tories have a good week, the Tories shoot up.

None of us can really be sure how public opinion would settle down if there were an early election.