Cabinet minister Nicky Morgan has revealed she would vote for Remain in a second referendum, leading to accusations of her “putting career before conscience” for continuing in her government role.

Despite serving in Boris Johnson’s administration – with a pledge to deliver Brexit by 31 October with or without a deal – the culture secretary added she was not “comfortable” with the result of the 2016 referendum at the time.

Appearing on the BBC’s Breakfast programme, Ms Morgan, who accepted a job in Mr Johnson’s cabinet in July, insisted she had accepted the EU referendum result and it was the duty of MPs and parliament to deliver on it.

But asked directly how she would vote in a second Brexit referendum, Ms Morgan replied: “I would vote to Remain.”

Pressed on why she was then serving in Mr Johnson’s cabinet, despite her own personal view, the minister continued: “It is not a result I was comfortable with but I have accepted it.”

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But the Labour MP David Lammy seized on her remarks, posting on his Twitter account: “Repeat after me. Nicky Morgan put her own career progression before her conscience, constituents and country.”

Later on BBC Radio 4’s Today programme, Ms Morgan insisted she did not support “having another referendum” and as a result “it’s not something I spend an awful lot of time dwelling on”.

“My instinct is that I’m sorry the Remain campaign didn’t win in 2016 and that really I’m sorry we’ve seen all the division and uncertainty over the last three and a half years.

Asked what motivated her choice to back Remain should there be a second referendum, she added: “Well I think the same reasons that I felt very firmly back in 2016 that I campaigned for Remain.

“Partly economic, partly more geopolitical devices that I felt that being part of the EU was so geopolitically the right decision.”

Justifying her decision to serve in Mr Johnson’s cabinet and stand by the commitment to leave without a deal should one not be in place by 31 October, Ms Morgan said: “I think generally in life when you’re offered an opportunity to serve in the cabinet it’s an element of public service.

“I think you should do what you can to accept that. I think the reason people ask these questions today is to misunderstand the nature of representative democracy and representation.