The deputy leader of the Liberal Democrats, Jo Swinson, will stand to replace Vince Cable as the head of her party, she has announced.

The party’s foreign affairs spokeswoman used an appearance on the BBC’s Question Time programme on Thursday evening to make the announcement and said she would officially launch her campaign the following day. She is the second person to announce their candidacy.

“I happen to think that this country is crying out for a liberal movement that will challenge the forces of nationalism and populism … the Liberal Democrats need to be at the heart of that movement, and I’m the person to lead it,” she told the Question Time audience.

Her announcement came after the former energy secretary, Sir Ed Davey, said he would run and pledged to work to revoke article 50 if elected. The announcement coincides with the publication of an opinion poll showing the Lib Dems in first place, with the Brexit party second and the Tories and Labour level in third.

Sir Ed Davey has also launched his campaign to become the next leader of the Lib Dems. Photograph: David Mirzoeff/PA

The YouGov poll for the Times suggested that 24% of voters would support the Lib Dems if a general election was held immediately, with 22% backing the Brexit party, and the two traditional parties of government on 19% each.

On Question Time, Swinson reiterated her backing for a second referendum, saying people should have the right to confirm their choice when they have a clearer picture of what Brexit would look like.

Swinson, the MP for East Dunbartonshire, who served as a business minister in the coalition government, was tipped as a frontrunner to replace Cable when he announced his intention to stand down as Lib Dem leader in March. The party’s education spokeswoman, Layla Moran, was also expected to stand, but ruled herself out of the running earlier this month.

Cable originally planned to stand down as leader after the local elections in May, but decided to stay on through the UK’s unexpected participation in the European elections. The party made a strong showing, garnering more than 20% of the vote. He will now relinquish the leadership on 23 July.