The concerns were exacerbated when former Conservative minister Owen Paterson used a BBC interview to float the prospect of a debate on restricting abortion rights as part of any DUP talks.

“Owen Paterson’s comments on the Today programme have caused real raised eyebrows," said Morgan, who has previously talked about how she changed her mind on social issues such as same-sex marriage.

"I have always believed we are stronger when we appeal to the middle ground."

Morgan also said the entire cabinet should be required to endorse any formal arrangement with the DUP to prop-up a minority Conservative administration.

"But I have grave reservations about a formal deal rather than a vote-by-vote arrangement," she added.

One Conservative MP told BuzzFeed News that the British public's attitude towards LGBT rights had changed so much in recent years that any association with the DUP could be toxic and cost the party votes, even in safe Tory seats. This election saw a record 45 LGBT MPs elected to parliament – including 19 Conservatives.

"I will knock on a door in a leafy village and they will say 'my nephew's gay – you've just joined with a party who hates gays'," said the MP. "Then I will spend 20 minutes explaining it's confidence and supply. By which time I've lost.

"There's a generation who do not understand how toxic it is. I'm not going to go down with this ship."

This MP said any alliance with the DUP could undo decades of careful neutrality by the Westminster government which has aided the Northern Ireland peace process. They said the cabinet should be forced to take collective responsibility for the deal: "Make sure that everyone's hands are dipped in blood. This needs to be a cabinet decision not a tactical leadership decision."

In reality, the MP said the issue was likely to come to a head in an angry meeting of the Conservative backbenchers' 1922 committee next week: "I'm buying popcorn makers because I'm going to make a fortune."