THERESA May was warned that her three Brexit priorities for Ireland were incompatible back in 2016, the UK’s former ambassador to the EU has said.

Ivan Rogers said he discussed the same dilemma with Boris Johnson, the frontrunner to become the next prime minister.

The former diplomat told Westminster’s Foreign Affairs Committee that May’s speech setting out her Brexit red lines prompted him to think they would cause a stir in Brussels.

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He also said he and then cabinet secretary Lord Jeremy Heywood had no sight of the address before it was delivered. Rogers said that in 2016 he delivered “one of the most unpopular things” he had told the PM. He said it was that “you have made three commitments in good faith to different audiences, but they are not really compatible with each other”.

“You have said to the Irish ... under no circumstances will a hard border be erected across the island of Ireland. You have said to the Democratic Unionist community under no circumstances will there be divergence from the rest of Great Britain.

“And you have said to the right of your own party that you are heading out of the customs union. You can’t do all three. You have got to choose two of the three.”

The backstop – a last-resort mechanism to prevent a hard border in the island of Ireland if no post-Brexit deal is negotiated – proved to be a major sticking point and helped lead to May’s demise as PM.

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In further evidence, Rogers discussed his shock at May’s red lines. She told the Tory conference in 2016 that any deal would have to include control of the UK’s borders, exiting the EU’s single market and not staying in the customs union.

Rogers, who quit as the UK permanent representative in 2017 after clashing with ministers over Brexit, said he “didn’t get any sight of it in advance”, despite seeing previous party leaders’ addresses.

“I didn’t see the speech. I, of course, thought the moment I did see it ‘blimey that’s going to elicit quite a reaction in Brussels’,” he said. “I did talk to Jeremy Heywood and say ‘did you see the speech, it’s a bit puzzling that we suddenly get landed with this and red lines which are really going to take people by surprise in Brussels.”