Their latest joint initiative left critics of the two leaders, in their respective parties, asking where would the ever-closer union end?
There was a flurry of speculation at Westminster that Mr Ashdown would soon be invited to sit in the Cabinet as part of a Lib-Lab coalition; that there would be an electoral pact between the two parties at the next general election, with the one most likely to beat the Tories given a clear run, before an eventual merger.
Such speculation is wide of the mark for the time being, at least.
Last night's statement was really about keeping on track Mr Blair and Mr Ashdown's shared goal of changing the landscape of British politics so that the two centre-left parties avoid the bitter rivalry which helped the Tories enjoy 18 years of hegemony.
Lib-Lab relations were strained by last month's report on proportional representation by a committee headed by Lord Jenkins. Mr Blair now appears to have convinced Mr Ashdown he is serious about electoral reform, although he will need time to persuade his party to buy it. So, Mr Ashdown was prepared to endorse closer links with Labour.
Both men are taking a risk because they will face flak in their own parties.
The sensitivity of the issue was shown when the fax machines whirred at Downing Street, and in Mr Ashdown's Commons office, as several proposed drafts of the statement went backwards and forwards in recent days.
Liberal Democrat MPs were sounded out about extending the remit of the joint Cabinet committee, on which Liberal Democrat leaders discuss constitutional reform with Mr Blair and his ministers, to cover health, education and welfare.
Some Liberal Democrat MPs reacted furiously, fearing that Mr Blair was seeking to stop their party attacking the Government's record on public services. There were even rumours that Simon Hughes would resign as the party's health spokesman if his freedom to criticise ministers was to be neutered.
So the final statement promised a review of the Cabinet committee to see how its work can be widened, rather than a firm list of new areas of co-operation. In the short-term, there may be ad hoc discussion of specific issues, such as pensions, rather than a wide-ranging agreement about welfare reform as a whole.
But Downing Street made clear that the Prime Minister believes that the Liberal Democrats input has helped the Government, and it wants them to influence policy on education, health, welfare and Europe.
Mr Blair chairs the Cabinet committee, which has met six times since it was set up in September last year, and is joined by a variable cast of Cabinet ministers depending on the agenda.
Mr Ashdown and his four members - Menzies Campbell, Alan Beith, Robert Maclennan and Lord Holme - sit on the opposite of the large, coffin-shaped Cabinet table. "It's not cosy at all; there is a lot of hard negotiating," said one Liberal Democrat source.
Despite such reassurances, the pledge of closer co-operation will fuel the sceptics in both parties. Labour left-wingers say they would rather form a breakaway socialist party with the trade unions than merge with the Liberal Democrats. Meanwhile, some of Mr Ashdown's MPs fear the Prime Minister is subtly trying to make them irrelevant.
"Blair is trying to smother us to death," said one. "The trouble is that he holds all the cards."Reuse content