With ballot papers going out, Mr Hughes is keen to capitalise on growing hostility in the party to Tony Blair's New Labour policies. The mood has already led to a wobble in Mr Kennedy's campaign - and could prove the decisive issue.
Mr Kennedy yesterday countered claims that he is cosying up to Labour by attacking the Government for following right-wing US-style policies of free-market economics.
Supporters of Mr Hughes and Jackie Ballard, another of the five candidates to take over from Paddy Ashdown on 9 August, have privately accused Mr Kennedy, the front- runner, of changing tack on links with the Government to match the anti-Labour sentiment in the party.
"Kennedy is back-tracking and flimflamming because he knows it's unpopular with the grass roots," said a Hughes campaigner. "Charles has sold his soul to Don Foster [the education spokesman] and the party establishment who like the whiff of power the joint Cabinet committee provides them with, but that is not going down well with the grass roots who have their heads kicked in by Labour activists."
Mr Kennedy, MP for Ross, Skye and Inverness West since 1983, has said he would not rule out further co-operation with the Labour Government, and this would include working together on Britain's entry to European Monetary Union.
Further areas allowing co- operation in this Parliament were unlikely, but he added: "We should not rule out the possibility."
In persuading Mr Foster to stand down from the race, there were hints that the joint cabinet committee on constitutional affairs should be widened, possibly to include nursery education.
Mr Foster, the strongest of the candidates in support of closer co-operation, said he had received "firm assurances" from Mr Kennedy about continuing co-operation before deciding to pull out and back him. Other MPs favouring co- operation, including Menzies Campbell, are also supporting the Kennedy campaign, but in recent hustings meetings Mr Kennedy has insisted that he would not extend further cooperation before the next general election.
Mr Hughes, MP for Southwark North and Bermondsey, exploited the apparent inconsistencies in the Kennedy campaign last week by challenging his main rival to clarify his policy over closer links with New Labour.
He coupled it with a warning to the party "grandees" that they risked alienating the party. "We've seen key establishments figures - a colleague described them as the party mafia - anoint their chosen candidate in the hope that he will pursue close relationships with Labour," Mr Hughes told a party meeting.
Mr Hughes's campaigners believe the race is now too close to call, with their man likely to get 49 per cent to Mr Kennedy's 51 per cent. He would hope to pick up most of the votes of Ms Ballard and David Rendel on second preference but the outcome in the single transferable vote may depend on where the votes of Malcolm Bruce are redistributed.