The Conservatives’ chances of retaining the Brecon and Radnorshire constituency in a byelection at the start of next month have slimmed after other pro-remain parties opted to stand aside to give the Liberal Democrat challenger a free run.

The Green party and Plaid Cymru said they had decided to not stand candidates in the Welsh seat on 1 August in the hope of maximising the vote for Jane Dodds, the Lib Dem hopeful.

The byelection was called after voters signed a recall petition against the incumbent Conservative MP, Chris Davies, who was convicted of submitting fake expenses documents. The petition was signed by 10,005 people, 19% of registered voters, well above the 10% threshold needed for a recall.

The Conservatives have since announced that Davies will stand again, while the Brexit party is also putting up a candidate, further boosting the chances of the Lib Dems regaining a seat they held from 1997 to 2015.

The Lib Dems are privately hopeful about winning the seat, which would instantly cut the effective working majority of the new Conservative prime minister to just three.

Jo Swinson, the Lib Dems’ deputy leader, who is standing as a candidate to replace Vince Cable as leader, tweeted her thanks to Plaid Cymru and the Greens, saying: “Putting the needs of the country above party politics takes courage.”

Adam Price, the leader of Plaid Cymru, told the BBC the decision was not easy, but had been “the right thing to do”.

He said: “We are facing one of the most significant decisions, as to whether we are going to be seemingly yanked out of the European Union even without a deal. Under those circumstances it is in Wales’s interest and our common interest to work together and coalesce the support for the remain side in Wales.”

Both Price and Cable said similar pacts were likely in future. “There is no doubt that the co-operation that this is generating could well lead to wider measures,” Cable told the BBC.

Davies secured a majority of just over 8,000 in the 2017 general election, with the Lib Dems in second, Labour third and Plaid Cymru fourth. In the byelection, the Brexit party is putting up a candidate who would be expected to take some Conservative votes.

Quick Guide Brecon and Radnorshire byelection Show Why was there a byelection? A petition to recall the Conservative MP Chris Davies secured the signatures of more than 10% of registered voters in the constituency. Davies was convicted for submitting fake expenses documents invoices for nine framed landscape photographs, costing £700, to decorate his office in Builth Wells. He was fined £1,500 and ordered to complete 50 hours of community service. He stood again for re-election. How did the parties do at the last election? In 2017 the results were as follows: Christopher Davies (Cons) 20,081 (Maj 8,038)

James Gibson-Watt (Lib Dem) 12,043

Dan Lodge (Lab) 7,335

Kate Heneghan (Plaid) 1,299

Peter Gilbert (Ukip) 576 What were the 2019 results? The Liberal Democrats took the seat from the Conservatives: Jane Dodds (Lib Dem) 13,826 (Maj 1,425)

Christopher Davies (Cons) 12,401

Des Parkinson (Brexit) 3,331

Tom Davies (Lab) 1,680

Lady Lily the Pink (Monster Raving Loony) 334

Liz Phillips (Ukip) 242

The idea of left-leaning or anti-Brexit parties standing aside for each other to avoid splitting the vote under the UK’s first-past-the-post parliamentary election system – known as a progressive alliance – was mooted before the 2017 election.

While a handful of candidates did step aside, the idea proved difficult to implement more widely, with parties often loth to order long-established activists to give up their hope of fighting the election.