Mr Ashdown asked delegates at a conference of Liberal Democrat councillors in Birmingham to work in greater co-operation with their Labour counterparts in local government.

The BBC's Laura Trevelyan: Poll's mixed message for Mr Ashdown

The move follows his recent decision to increase co-operation with Labour on the joint cabinet committee examining constitutional reform.

Mr Ashdown has also signalled that he would like to see greater links on other issues.

In an article in a forthcoming issue of the Parliamentary House Magazine, he has written: "If we and the government can identify some specific project-based areas for further co-operation beyond the constitutional reform agenda of the Joint Consultative Committee, then we will do so.

"There has been enormous progress over the last year, and the time is right to look at other areas where our aims coincide and where constructive engagement can bear real fruit."

'Private talks'

After what were described as "private" talks with Mr Ashdown, Sarah Boad, the Chairman of the Association of Liberal Democrat Councillors, said: "This has been a very successful and positive meeting.

"We were very pleased he took the time to come and hear our views. Not everyone agrees, of course, but we have had a chance to put our questions to him. It is a leadership style we appreciate."

The conference also heard from party chief whip Paul Tyler who urged closer working with Labour.

"I rejoice in our unexpected influence in this Parliament. I relish the impotent fury aimed at the Liberal Democrats by the old Labour Left and the older still Tory right," he said.

"Of course there are risks. Which of you has created working arrangements with another party group in the council without risk?"

'Very encouraged'

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However, the survey, carried out for BBC Radio 4's Today programme, found 44% of the Liberal Democrat constituency party chairmen who responded wanted to see a vote of all party members on a new relationship with the government.

Another 48% said party members should not be balloted. The remaining 8% said they did not know or declined to answer.

On whether they thought the party benefited from closer links with Labour, 56% thought it did, while 26% did not.

Liberal Democrat Head of Campaigns, Nick Harvey MP, said he was "very encouraged" by the poll results.

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There was "some surprise on all parts" when plans for closer co-operation with Labour were announced, but the overwhelming majority of party members were now in favour, he said.

"I think as the debate continues more and more people will come to the same solution."

Leadership challenge

Mr Harvey also dismissed claims that Mr Ashdown faced a threat to his leadership after 27 of the 205 constituency chairman questioned said they wanted to see a challenge.