Nicky Morgan has said she would vote to remain in the EU if there were to be a second referendum.

The culture secretary, who campaigned for remain in the run-up to the 2016 poll, said on BBC Breakfast she would vote the same way again.

Morgan originally said she did not support holding another poll and believed the original result should be accepted. When asked how she would vote if the public were asked directly again, she said: “I would vote to remain.”

All opposition parties support a second referendum. When pressed to clarify why she was serving in Boris Johnson’s cabinet if this was her view, she said: “It is not a result I was comfortable with but I have accepted it.”

She later told BBC Radio 4’s Today programme: “I feel very firmly that the result of the 2016 referendum needs to be fulfilled and that’s why I’m in the cabinet and that’s why I support Boris Johnson’s determination to make sure that we do leave the EU by 31 October, preferably with a deal.

“My instincts are that I was sorry that the remain campaign didn’t win in 2016 and that really I’m sorry that we’ve seen all the division and uncertainty over the last three-and-a-half years.”

She said her views on the matter had evolved because she could now “see a way for the UK to leave the EU and to do it with a deal and to strike out in different ways in the rest of the world”.

In an interview with the Times, David Cameron accused Johnson and Michael Gove of effectively “trashing” the government during the 2016 campaign and said a second poll could not be ruled out “because we’re stuck”.

Responding to the former prime minister’s comments, Morgan told ITV: “I don’t think it’s actually very helpful to keep rerunning the 2016 campaign and who said what, when. The fact is, we had a result and actually it’s incumbent on those of us who are in government, still MPs, to make sure that result is delivered.”

Morgan said she had been very clear that she would vote to remain but did not support a second referendum.

In response to Morgan’s comments, the Labour MP David Lammy tweeted:

David Lammy (@DavidLammy) Repeat after me. Nicky Morgan put her own career progression before her conscience, constituents and country. pic.twitter.com/5J76bv2oE0

The former Brexit secretary David Davis also suggested on Saturday that the government might have a legal strategy to avoid extending Britain’s EU membership beyond 31 October, despite the so-called Benn Act to avoid no deal.

The legislation, which received royal assent earlier this week, would require the prime minister to seek an extension unless a deal is approved or parliament agrees to leave the EU without a deal by 19 October.

Davis told BBC Radio 4’s The Week In Westminster: “I think there may well be a legal strategy – I’ve no idea what it is – but I think that may well be the way through, to effectively legally kill off the Benn bill [sic] and then find a way of coming back to the negotiations with a real sword of Damocles over them, the Europeans, rather than over us.”

Johnson has repeatedly said he would take Britain out of the EU at the end of next month, and that he would rather be “dead in a ditch” than ask for an extension.