The Prime Minister is convinced that the links will continue to grow regardless of who takes over as the new leader of the Liberal Democrats and despite fierce opposition from some MPs in both parties.
Mr Blair has privately made it clear that he could work with Charles Kennedy, who is regarded as a front runner in the leadership contest, although he remains wary of endorsing any of the candidates in public.
Mr Kennedy, who has already won the backing of Lord Jenkins of Hillhead, one of the Prime Minister's "mentors", has publicly expressed doubts about "cosying up" to Labour in the past. However, Downing Street believes that he would not abandon the "project" started by Mr Blair and Mr Ashdown if he took the helm. "It looks like Kennedy is where it's going to end up," one friend of the Prime Minister said. "I don't think we would have any trouble with Kennedy at all."
Mr Blair has asked Jack Cunningham, the Cabinet "enforcer", to meet Alan Beith, the Liberal Democrat's deputy leader, to work out new aspects of government policy which could be brought within the remit of the Joint Cabinet Committee which is currently considering constitutional reform and defence.
Insiders say welfare, education and health are top of the agenda. According to allies, Mr Blair also has "a lot of time" for Menzies Campbell, the Liberal Democrat foreign affairs spokesman, who has been heavily involved in the Joint Cabinet Committee.
The leadership contest will not begin officially until after the European elections in June. But potential candidates have already mounted vigorous campaigns behind the scenes. All the contenders are manoeuvring to be seen as supporters of closer ties with the Labour government because they believe that the 105,000 Liberal Democrat members who will elect the new leader are in favour of co-operation. Even Simon Hughes, who voted against closer links with Labour, said last week that he was not against working with Mr Blair.
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