The Liberal Democrat leader, Jo Swinson, will embark on a summer campaigning blitz to position herself as a viable alternative prime minister, as sources suggested the independent MP Sarah Wollaston could join at the party’s autumn conference.

Swinson, whose party is hopeful of winning a byelection in Brecon and Radnorshire next week, will do a tour of the UK over August as well as ramping up fundraising and logistical planning for a snap election, the Guardian understands.

Labour rejected calls from Swinson to trigger a vote of no confidence in Boris Johnson on Thursday, saying she knew it would not succeed and calling the move “childish and irresponsible game playing by the Lib Dems who are more interested in attacking Labour than stopping no deal”.

The Labour leader, Jeremy Corbyn, also had a dig at the Lib Dems in his early exchanges with Johnson after the prime minister’s statement on Thursday, saying: “Youth centres have closed, their school funding has been cut and their college budgets slashed, and with the help of the Liberal Democrats, tuition fees have trebled.”

The Guardian understands that there are now firmer plans for Wollaston, the Totnes MP who defected from the Tories to Change UK and then left this summer, to follow Chuka Umunna and join the Lib Dems this autumn, perhaps as soon as party conference in September.

Wollaston had been waiting for Swinson to be confirmed as Lib Dem leader. She has told friends she did not want to make a hasty next move but is known to be close to Swinson. Wollaston may only be prepared to run as the party’s candidate at an election if she is able to stand on a “remain alliance” platform, whereby the Greens stand aside on the proviso she will run for the Lib Dems with a series of pledges on the environment.

It is possible that if either local party objects, she would choose not to stand against their preferred candidate.

The Devon seat has a mixed demographic including left-leaning, pro-remain inhabitants of Totnes, but also a heavily Brexit-voting rural and coastal population.

Wollaston, who was selected via an open primary for the Tories, has a majority of 13,000 but the Conservative vote may be significantly affected if the Brexit party were to run in the constituency, which has been heavily targeted by the Leave.EU co-founder Arron Banks.

The seat has been a Lib Dem-Tory marginal as recently as 2005 though the Lib Dems were overtaken by Labour at the 2017 election. The Conservatives have already selected Anthony Mangnall, the special adviser to the Welsh secretary, Alun Cairns, as their candidate in the seat.

It had been reported that Umunna could switch to run in Vince Cable’s seat of Twickenham if the former Lib Dem leader steps down at the next election. However, senior Lib Dem sources said there was a firm feeling in the party that the new recruit should be able to fight and win Streatham, which he won for Labour in 2017 with a majority of more than 26,000.

“The polling looks very good for us in that area and there is no reason why we could not win that seat,” one senior source said. “Many of us remember campaigning against Chuka when Streatham was a target seat for the Lib Dems in 2010.”