John McDonnell has said he will not stay neutral in a second EU referendum vote as Labour sought to clarify the party’s Brexit strategy with less than three weeks until voters go to the polls.

In an interview on Sunday, the shadow chancellor said he and fellow cabinet members will be able to campaign for either side in a referendum if they form the next government.

His comments follows Jeremy Corbyn’s declaration on Friday that he would be an “honest broker” and neither campaign to leave nor remain under a Labour administration.

McDonnell’s words came as Jo Swinson, the Liberal Democrat leader, acknowledged that Boris Johnson was on course to win an overall majority in the general election on 12 December.

McDonnell told Sophy Ridge on Sky News that Corbyn would allow individual members of the cabinet to campaign on the basis of their judgment. “Members of the shadow cabinet, well, members of the government then, will be able to campaign,” he said.

Asked whether he would stay neutral, he said: “No, I won’t and I don’t think Jeremy’s asking people to do that. I’ll wait until I see the details of the deal that we negotiate. I’ve said up until now – I was in the negotiations with the Conservatives for six weeks and I couldn’t see a deal even emerging then that could beat remain, but let’s see what we can negotiate.”

Corbyn has promised to negotiate a new Brexit deal with the EU and put this to a public vote alongside the option of remain. He has defended his decision to remain “neutral”, saying it is a sign of “strength and maturity”.

The polls have not improved for Corbyn following the launch last week of Labour’s manifesto, showing the Tories with a 19-point lead over Labour.

In an interview with the BBC’s Andrew Marr Show, Swinson said: “As things stand, Boris Johnson is on course to get a majority.”

Her party has the best chance of scuppering that majority and avoiding a hard Brexit, she said. She pointed to recent polling in the seat of Great Grimsby that showed Labour could be about to lose the seat to the Tories, having held it since the second world war.

“If you are a remain voter, the last thing you want to happen is for Boris Johnson to win a majority to see through his hard Brexit deal that could turn into a no-deal Brexit in just over a year,” she said.

On the same programme, Michael Gove, the chancellor of the duchy of Lancaster, ruled out asking for a further Brexit delay to secure a new trading relationship with the EU.

Asked whether a Conservative government would ask for an extension, he replied: “No … we’ll be out of the EU by January. We will have formally left.”

He was shown a clip of Boris Johnson’s aide Dominic Cummings speaking in 2017, in which he said Tory MPs largely did not care about poor people or the NHS. Responding to the clip, Gove said: “He’s wrong about that. There are a number of occasions where I’ve disagreed with Dominic on this issue and some other matters as well.

“I’m very happy to look at our record in government.”