I doubt whether Gordon Brown's interview with The Guardian was intended to smoothe the way for his early retirement, but it has been taken that way, particularly by other newspapers. There was a note of regret in what he said. “It wouldn't worry me if I never returned to any of those places - Downing Street, Chequers.” His interview would fit in with preparation for an early resignation, if that became necessary; experienced politicians like to create options for themselves that they will not necessarily take.

Conservative MPs see the possible advantage for Labour of an early election. Eric Pickles, the Conservative Party chairman, said last week that the party was drawing up contingency plans for an early election, which would include the resignation of Mr Brown. The Tories will not be taken by surprise.

The scenario would work something like this. Mr Brown would have to resign some time before the summer recess, which will start on July 21. There would then be an election for the new leader, which would be completed in about six weeks. The new leader would benefit politically from the recess, which usually gives a welcome respite to parties under pressure.

In his or her speech to the Labour Party conference, the new leader would announce the dissolution of Parliament and open the general election campaign. The election day would come in mid-October; the Conservatives would see their conference largely submerged by the opening of the campaign.

The choice of date for the election lies between mid-October and May 2010. It is hard to see how the six-month gap between October and May would help Labour. The summer recess may calm public opinion, but the political atmosphere is now so bad that the constitutional issue and failures of Parliament will still preoccupy MPs after the recess. The new leader, if there is a new leader, is likely to be more popular in the first weeks than after six months. There would be a short honeymoon, if not much enthusiasm.

Polls show that voters want an early election. They are likely to become more and more resentful if they have to wait until next May. That would show that the Government had not understood the national anger. Peter Hennessy, the professor of contemporary British history, takes the view that it will be ten years before Parliament regains public confidence. That will certainly require a new Speaker, who will be elected today, a new Parliament and a new prime minister, even to begin the process. From Labour's point of view, the nightmare would be to wait for a May general election with Mr Brown still leader.

The Conservative lead in the opinion polls is at present so wide that Labour could expect to lose 150 to 200 seats in a May election under Mr Brown. Only an early election and a new leader are likely to change that arithmetic.

There is, however, one obstacle. Last week in Brussels Gordon Brown was negotiating with Brian Cowen, the Irish Prime Minister. Their subject was the second Irish vote on the Lisbon treaty, which was rejected by the first. Mr Cowen has secured a new protocol for Ireland to persuade the Irish to vote “yes” at their next referendum. The protocol would give Ireland a guarantee that the treaty would not affect the Irish system of taxes, the Irish laws on abortion or the Irish freedom from defence commitments.

Mr Cowen seems to have got his guarantees, but Mr Brown apparently avoided changes in the treaty that would require further ratification. David Cameron has made it clear that he would hold a British referendum if Lisbon had not been completely ratified when the Tories came to power. The British would almost certainly vote “no” if they were allowed the referendum, which was promised by all three parties in the 2005 general election.

Apart from Ireland, at least three other nations have not yet completed the process of ratifying Lisbon. German ratification is subject to the constitutional court, which has to satisfy itself that Lisbon is compatible with German democracy. Poland and the Czech Republic require the signatures of their presidents.

Václav Klaus, the Czech President, has threatened not to approve the new guarantees for Ireland. That could delay Czech ratification even if Ireland votes in favour. In any case, Mr Klaus might delay further if Mr Cameron wins office.

Beyond that, there will be the ratification of the Irish protocol. Britain has completed the parliamentary procedure of ratifying the Lisbon treaty itself, but has not ratified the new guarantees for Ireland. Again, the Conservative Party, if it came to office before the Irish protocol was ratified, might call a referendum on that protocol.

These problems all arise from Mr Brown's refusal to hold the British referendum that Labour promised; they make the timing of the British general election and the Irish referendum crucial to the ratification of the treaty. To complete the Lisbon process, the Irish referendum needs to be held as early as possible and a British general election as late as possible. If the Irish referendum and the British general election were both held in early October, there would not be time to complete the ratification of Lisbon before Britain had the opportunity to hold a referendum.

There are two reasons why this is so important. Lisbon is genuinely a federalising treaty, a rewriting of the European constitutional treaty, which was rejected by France and the Netherlands in their national referendums. The treaty transfers power from national parliaments to the Brussels bureaucracy and would make Britain a province of a European state with a European president. The British do not support such a treaty, but have never had the opportunity to vote on it. October 2009 would be the best window of opportunity for Labour. Will Labour sacrifice their best election chance to protect the Lisbon treaty?

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