Shadow chancellor John McDonnell has said he is hoping that the next leader of the Labour Party will be a woman.

The Labour frontbencher told Mumsnet he was “anxious” about another EU referendum and would much prefer a general election, adding that his party would “keep all options on the table”.

Undertaking an hour-long webchat, Mr McDonnell, who has been tipped by some as a possible Labour leader, answered questions on topics ranging from Brexit, Russia and anti-Semitism to allegations of nepotism and de-selections.

Mr McDonnell said the issue around anti-Semitism “should have been handled much more effectively and sooner”, adding that he hoped the party “can move forward on this issue much more constructively”.

He also said Labour needed to “build bridges with the Jewish community”.

A Labour General Election win, he said, was “achievable”, and added that the party “respects” the EU referendum result.

On Labour’s six Brexit deal tests, he wrote: “If they are not met by whatever Theresa May brings back from Brussels, then we will not vote for the deal.

“My view, then, is that we should have a general election because, in a general election, people can not only debate the range of issues in full, they can also select the team that will then negotiate our future position.

“If we can’t get a general election, we are keeping the option of another vote – a people’s vote – on the table.”

He added: “We have to somehow bring the country back together again and I think the best way of doing that is to seek to reach a traditional British compromise on the basis of a constructive deal with our EU partners – one that maintains a close and collaborative relationship with the other EU countries that we can build upon.

“I believe that our European partners would be up for that sort of co-operative deal.”

Mr McDonnell also defended his employment of Jeremy Corbyn’s son Seb, adding: “He was appointed on merit and I regret the level of abuse he’s received just because of his surname… I do not believe that people’s families should be brought into political debate in this way.”

He said he was “really worried” about the state of social media, adding: “People seem to think they can say anything on social media often in ways they would never say to your face. I just find we all need to stand back a bit and think hard about how we communicate and the reaction of people to our words. That includes me.”

Mr McDonnell said he planned to publish a detailed budget setting out the party’s spending plans which he would then consult the wider community on.

The MP for Hayes and Harlington expressed his support for the idea of having job-sharing for MPs, adding the party was continuing with all-women shortlists for selections, adding: “I think there is support for maintaining the trigger system with a bit of reform, I think that is the right balance. So it’s not about de-selections, it’s about making sure we have (an) effective democratic process for choosing our candidates and for local party members to express a view.”

Asked if the UK could repair relations with Russia in the wake of the Salisbury attack, he said: “Of course… but I believe we can be more effective by the use of orders to tackle the Russian money that is flowing through the City of London, often in money laundering exercises.”

Answering the customary Mumsnet question on his favourite biscuit, Mr McDonnell replied: “My Mum worked behind the biscuit counter in BHS and we lived off broken biscuits, in particular rich tea.”