If there was one formula utterly calculated to infuriate the Chancellor, then this was it.

In private dicussions with Mr Blair — there were two meetings yesterday — Mr Brown has always argued that the new leader should be able to take over at a time when he was most likely to give the Labour Party fresh momentum and himself a “bounce” in the opinion polls.

He is also waiting for public signs from Mr Blair that the “stable and orderly” transition is under way, and wants Mr Blair to try to stabilise the current turmoil by repeating the pledges of his senior ministers that he will, indeed, go next year. The time for coded messages is gone, Mr Brown believes.

Yesterday it is believed that he urged Mr Blair to say more in order to clear the air, but he is not pressing him to go immediately.

Friends said that Mr Brown was desperate for there to be a bloodless transition and that he would be badly damaged if he was seen to come into the job as a result of a coup or plots by his supporters.

But the idea that Mr Brown would come to power next summer just as MPs were leaving Westminster and the country going on holiday was laughed off in Brownite circles yesterday.

Among Brownite MPs, the May-July formula was seen as an “opening bid” from a Blairite team that now recognises that their man has a limited time left in office.

But taking over as Parliament went into recess would deprive Mr Brown of any chance of marking his arrival with new legislation — for example to increase the 28-day detention period for terrorist suspects up to 90 days.

Mr Brown is aching to take on David Cameron at the House of Commons dispatch box. So what sense would there be in taking over at a time when he would have to wait for another three months before he could get at the Tory leader? And, if Mr Brown, who has a keen sense of history, is hoping to be judged on his first 100 days in office, how would that be helped by him taking charge at a time when most people switch off from politics and even stop reading their newspapers? As Mr Brown’s closest supporters yesterday weighed the implications of the past traumatic week, most of them agreed that their man’s best interests lay in Mr Blair announcing soon that he will be going — perhaps in January next year.

That would enable the Chancellor to fight a leadership election, to win it, and to take over well in time for the Scottish and Welsh elections taking place early in May.

If Mr Blair were to hang on until then, those polls would be treated as a referendum on an outgoing prime minister and, as such, be disastrous for Labour. But, if Mr Brown took over well before, the voters would be able to ponder the new administration and make a judgment on the new Prime Minister.

However, there were no early signs yesterday that Mr Blair was ready to fall in with that timescale.

A second option would be for Mr Blair to announce before the Scottish and Welsh elections that he was going, take the rap for bad results, and allow the new leader a clean slate.

A third idea, which would not be totally against Mr Brown’s interests, would be for Mr Blair to announce his departure immediately after those elections and quit after a leadership election some six weeks later.

That would give Mr Brown time to take over well before the next summer recess, get to grips with Mr Cameron and introduce some startling initiatives as he hits the ground running after his long, long wait.

Mr Brown’s main demand on Mr Blair is for him to deliver evidence that he is taking the transition seriously. What Brownites saw as Mr Blair’s brutal treatment of Tom Watson yesterday was against the spirit of a peaceful transition in their eyes.

They also want Mr Blair to rein in his “outriders”, such as Stephen Byers and Alan Milburn, who they feel are using the changeover as a chance to snipe at Mr Brown and try to encourage an ABG (Anyone but Gordon) candidate to emerge.

Times Recommends

• Swine flu vaccine for all as drug rushed through
• Artificial sperm and the race to build a baby
• BBC jets out stars to tout for prizes