Sir Vince Cable says the by-election in Mid Bedfordshire could “potentially be a mess” if his party and Labour split the vote in the Conservative stronghold.

The seat is up for grabs after the exit from the Commons of Nadine Dorries – the Tory MP who eventually stood down after 81 days in anger over a report into Boris Johnson lying to parliament over partygate.

Both the Lib Dems and Labour have been throwing their campaign machines at the seat, with both insisting they can win the mid-term ballot on 19 October.

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But Sir Vince – a former party leader and minister in the coalition government – warned “short-term tribalism” could see the Tories sneak over the line, and the two competitors should be talking to each other.

Speaking at a fringe event at the Lib Dem conference in Bournemouth, he said as “an eternal optimist”, he thought such an outcome would be “potentially an important educational experience” to laughter from members.

He added: “Let’s imagine that Labour and the Lib Dems do very, very well – so well that the Tories hold the seat. Well, that will be a message to everybody that if we mess up and engage in short term tribalism in the next election, there will be quite a lot of seats that finish up like that .

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“So that will hopefully will do a powerful persuasion job on both our party and the Labour Party to get our priorities right.

“And similarly if Labour or us do spectacularly badly – which I think is very unlikely, but it could happen – that would be an educational lesson on picking our priorities more carefully. We got this terribly wrong at the last general election and we must not do it again.”

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Asked by Sky News whether a wider deal should be made between the Lib Dems and Labour at the next election, Sir Vince said: “We’re not talking about deals. What is happening already and will happen in the general election is a good deal of tactical voting because the British voting system is horribly unfair.

“And you know, the voters understand that if they want to get rid of this government, they will have to choose Liberal Democrats or Labour depending on who has the best chance of winning. So it’s something coming in from the bottom, not imposed from the top.”

However, asked about the impact of the party’s announcements across its conference this week, the former business secretary said: “Lib Dem ministers played their role in the time of national crisis [during the collation years] and we would again.”

The campaign in Mid Bedfordshire has made its own headlines after tensions arose between the two parties.

Labour’s shadow science secretary Peter Kyle – who has been leading on the ground in the constituency – accused the Lib Dems of “deeply personal” attacks on their candidate, Alistair Strathern, telling The News Agents podcast: “I sense a style of politics by the Liberal Democrats in Mid Bedfordshire which is reminiscent of the campaign they ran against Peter Tatchell in the 1980s.

“I have no doubt that they are so desperate to make an impact in Mid Bedfordshire that if our candidate was gay, they would be doing a family values campaign. The moral high ground does not count for the Liberal Democrats in the way they are acting in that constituency.”

But the Lib Dems hit back, calling the comments “stupid and deeply insensitive”.

Asked if campaigning had been too “personal”, Lib Dem candidate and local councillor Emma Holland-Lindsay said: “On the doorstep, people are saying how positive we are.

“After one door knock, a man said he wanted to meet [me]… so I went round and he hugged me and described my campaign as refreshing.”

But had the attacks been aimed at Labour rather than the incumbent Conservatives?

“The anger levels amongst life long Tories is palpable,” she told Sky News. “We have focused a lot on fighting the Tories – on health services, on cost of living, on sewage.”

A senior Lib Dem source added: “It has been a positive campaign… so we have no idea what that particular MP is talking about.”

The Conservative candidate running for the seat is Bedfordshire’s current police and crime commissioner, Festus Akinbusoye.

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