Theresa May has told politicians not to make promises they can't keep, in a veiled warning to the two men vying to replace her as prime minister.

Making likely her final major speech before she hands the keys of 10 Downing Street to her successor, the Prime Minister also warned of a "coarsening" of public discourse and "tribal bitterness".

She urged political leaders to enter into the "spirit of compromise" as she prepares to begin her final seven days in office.

In what will be perceived as a dig at Tory leadership frontrunner Boris Johnson, May cautioned against "making promises you cannot keep" and "just telling people what you think they want to hear".

Johnson and leadership rival Jeremy Hunt have both pledged to try to renegotiate a Brexit deal with Brussels that does not include the contentious Irish backstop - something the EU has said is impossible.

The former London mayor has also vowed to leave the EU on October 31 "come what may", and has claimed the chances of a no-deal Brexit are a "million to one against".

In a speech at London's Chatham House, May defended her thrice-defeated EU withdrawal agreement as one which "delivered on the vote of the referendum... while also responding to the concerns of those who had voted to remain".

Speaking on Wednesday, she continued: "The problem was that when it came time for parliament to ratify the deal, our politics retreated back into its binary, pre-referendum positions - a winner-takes-all approach to leaving or remaining.

"And when opinions have become polarised and driven by ideology it becomes incredibly hard for a compromise to becoming a rallying point."

May added: "I believe that seeking the common ground and being prepared to make compromises in order to make progress does not entail a rejection of our values and convictions by one iota, rather it is precisely the way to defend them.

"Not by making promises you cannot keep, or by just telling people what you think they want to hear, but by addressing the concerns people genuinely hold and showing that co-operation, not absolutism, is the only way to deliver for everyone.

"For the future, if we can recapture the spirit of common purpose - as I believe we must - then we can be optimistic about what together we can achieve."

The Prime Minister said she was concerned about the state of politics in the UK and around the world, warning that absolutist politics meant some were losing the ability to disagree in a civil way, potentially leading to a "darker place".

"An inability to combine principles with pragmatism and make a compromise when required seems to have driven our whole political discourse down the wrong path," she said.

"It has led to what is, in effect, a form of absolutism- one which believes that if you simply assert your view loud enough and long enough you will get your way in the end.

"Or that mobilising your own faction is more important than bringing others with you. This is coarsening our public debate.

"Some are losing the ability to disagree without demeaning the views of others.

"This descent of our debate into rancour and tribal bitterness, and in some cases even vile abuse at a criminal level, is corrosive to the democratic values which we should all be seeking to uphold."

The PM added: "Words have consequences. And ill words that go unchallenged are the first step on a continuum to ill deeds.

"Towards a much darker place where hatred and prejudice drive not only what people say but also what they do."