Vince Cable has set the date for his departure as Liberal Democrat leader, saying he will hand over a “bigger, stronger party” to his successor on 23 July.

With the party expected to do well when the results of Thursday’s European elections are announced on Sunday, Cable said it was time to fulfil his promise to step aside.

The contest to succeed the 76-year-old former business secretary features the former business minister Jo Swinson and the former energy secretary Ed Davey among the frontrunners. Lib Dem MPs can be nominated up until 7 June, which is also the cut-off date for new members to join the party in order to vote in the contest.

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Cable’s announcement came on the same day as Theresa May’s resignation from the Tory leadership – and the two contests are likely to overlap.

Although the Twickenham MP had said he would not stand down until Brexit had been “resolved or stopped”, he said in March that “it now looks as if it will be a protracted process” and that he would step aside before the summer.

He told party members in an email: “Our long and proud tradition of success in local government was revived this month by the best local election results in our party’s history. In the last two years, we have gained 780 more council seats and 15 new councils.”

Cable said he hoped his successor would build on “the opportunity created by the conflict and decay within the two main parties to build a powerful, liberal, green and social democratic force in the centre ground of British politics. We are now in an excellent position to lead such a movement”.

Cable had hoped his party would cooperate with Change UK, the fledgling party set up by breakaway MPs from Labour and the Conservatives, in the Peterborough byelection next month, but the discussions have foundered. However, with Change UK languishing in single figures in the opinion polls, a tie-up with the Lib Dems could appear more attractive.

The Lib Dems’ president, Sal Brinton, thanked Cable for leading the party “during the most tumultuous time in British post-war politics”.

She added: “Vince’s calm and mature leadership of the Liberal Democrats has helped us gain hundreds of seats in local elections and take control of councils up and down the country, as well as surging in the polls leading into the European elections”.

Cable inherited the leadership after an underwhelming performance at the 2017 election under Tim Farron, whose campaign was dominated by a row over whether he believed gay sex was a sin.

Cable’s early days in charge were fraught with difficulty, including a party conference speech in which he fumbled a planned reference to the “erotic spasms” sought by hardline Brexiters, calling them instead “exotic spresms”.