But the dark horse in the race to succeed Ms Mowlam is the Welsh Labour MP for Torfaen, Paul Murphy, who has been her trusty minister of state. Quietly spoken and little known in England, Mr Murphy has impressed Tony Blair with his grasp of the minutiae of negotiating with the disparate political parties in Ulster.
Until recently, Mr Murphy was expected to succeed Alun Michael as Secretary of State for Wales when Mr Michael vacates the post to concentrate on his position of First Minister of the Welsh Assembly. Many now think this post could go, instead, to Peter Hain (Neath) as a sop to Welsh "core" activities. In any event, Mr Blair owes Mr Hain a favour for delivering the Welsh Labour leadership to Mr Michael in preference to Rhodri Morgan.
Such a move would enable Mr Blair to capitalise on Mr Murphy's patient unflappability by both retaining him in Northern Ireland and granting him his much deserved promotion. Speaking after the collapse of the peace process, Mr Murphy hinted that the Government should "learn from mistakes" and implied that future negotiations should not be constrained by artificial deadlines.
THE CONSERVATIVE Party chairman, Michael Ancram, was cursing his diary before he faced a Press Gallery lunch, as guest of honour, on the very day hungry lobby journalists were anxious to bite chunks out of him over the business activities of Michael Ashcroft, the Tories' embattled billionaire treasurer.
Batting on a sticky wicket Mr Ancram nevertheless won over his sceptical audience with a self-deprecating sense of humour. He is about to become a fitness fanatic, having bought himself a tracksuit to jog into Conservative Central Office each morning. "I haven't worn it, but I feel better when I look at it," he said. Mr Ancram normally takes 20 seconds to walk to work - he lives next door to party HQ - "Ten seconds if it's raining and then I run: that's when I'll wear the tracksuit."
Mr Ancram recalled his discussions, as a former Northern Ireland minister, with The Rev Ian Paisley, who was angered by the Tory government's policies and predicted Mr Ancram would be buried in a "Sadduceean grave". Perplexed, Mr Ancram inquired what this meant. "A burial from which there is no resurrection," bellowed Mr Paisley. On hearing of Mr Ancram's appointment at Tory Central Office, Mr Paisley said: "I told you that you would suffer a Sadduceean burial." He used the phrase again this week in Stormont as he called for the Good Friday Agreement to be buried.
LABOUR MPs were even more sycophantic than usual during Prime Minister's questions. Even the normally independent-minded Alan Simpson (Nottingham South) caught the "reshuffle bug". "I am glad that we have been reminded that the reshuffle is in the air and I hope the Prime Minister will not presume that I am growling for preferment if I bowl him a soft one."
Mr Blair's response was suitably tantalising. "My honourable friend should not be so modest. It was such a good question that he should keep his pager with him at all times." The House collapsed but Mr Blair, probably reminding himself of Mr Simpson's normal rebelliousness, added:"That is not a promise."
One who needs to keep her pager switched on to be told that her services are no longer required might be the Transport minister Glenda Jackson. The strain of coping with the horrors of London Underground is proving too much and she finally slipped during transport questions. Accusing the Tory spokesman, John Redwood, of being an "ignoramus" she was brought up sharp by an angry Speaker who slapped her down with "that was quite unnecessary" and ordered her to withdraw the offending description. It was not as though Mr Redwood had even said anything during the exchanges. Next week could see Ms Jackson as the ignoramus.
AUSTIN MITCHELL (Lab, Great Grimsby) has gone all sentimental in his old age. Next week he publishes abook, Farewell My Lords, an affectionate look at the House of Lords. Previously committed to the abolition of the Upper House, he has even become a convert to the case for the hereditary peers. Interviewing more than 50 life and hereditary peers from all sides, "the charm, anxieties and concerns and the overwhelming niceness of the peers I talked to ensured I became increasingly sympathetic to a life form and an institution I previously regard-ed with amused indifference".
Cries of "coming to join us?" and "looking over the place ready for your retirement?" greeted Mr Mitchell on some of his trips down the corridor. Peers even invited him to their stately homes until he pointed out that they were the class enemy of New Labour - "the only one".