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.
Sir Ivan Rogers also said he discussed the same dilemma with Boris Johnson, the frontrunner to become the next British prime minister.
The former diplomat told the Foreign Affairs Committee on Tuesday that Mrs May's speech setting out her Brexit red lines prompted him to think they would cause a stir in Brussels.
He said that he and then cabinet secretary Lord Jeremy Heywood had no sight of the address before it was delivered.
Sir Ivan said that in 2016 he delivered "one of the most unpopular things" he had told to 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 agreement 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 Mrs May's demise as prime minister.
Sir Ivan also said he issued Tory leadership contender Mr Johnson with the same warning when he was foreign secretary.
Meanwhile Dominic Grieve has accused Mr Johnson of further radicalising on Brexit and leaving the UK with "starker" prospects by trying to appease hardliners in a strengthening of his stance on the Irish backstop.
The former attorney general also accused the Tory leadership front-runner of making a "disgraceful" suggestion which would spell the end of democracy as we know it.
On Tuesday, Mr Grieve warned whoever becomes the next prime minister that their government will collapse if they pursue a no-deal departure from the EU.
The day before, Mr Johnson said in a head-to-head debate with leadership rival Jeremy Hunt that the backstop to prevent a hard border in Ireland could not have time limits or "unilateral escape hatches".
Mr Grieve said Mr Johnson confirmed that hardliners would "put up another obstacle" if anyone was able to solve the issue because it is being "used as an excuse because of this radicalisation".
"When challenged and confronted, he radicalised even further and excluded any possibility of trying to negotiate some way out of the backstop at all. It had to go in its totality," Mr Grieve said.
Speaking alongside Mr Grieve at a second referendum campaign event, Labour MP Margaret Beckett called the candidates' backstop pledges "terrifying" and accused them of throwing "the Irish situation under a bus".
"Nobody can say that that situation is now so peaceful it's inconceivable that there will be further problems in the future. I think that's an extraordinary demonstration of lack of responsibility to the country," she said.
