Theresa May has issued a plea to the Conservative party to remain true to its traditional values after she bows out as their leader in a month’s time.

And in an apparent warning to Boris Johnson not to give ground to the populist and nationalist right, the prime minister said she wanted the UK to retain a spirit of “international co-operation and compromise” after she has gone.

She also said she wanted her successor – either Mr Johnson or Jeremy Hunt – to deliver a Brexit outcome which is “in the national interest”, something which she has repeatedly said requires a deal with Brussels.

Ms May’s comments, at the conclusion of the G20 summit in Japan, come shortly after an opinion poll which found a majority of party members would prefer to see the United Kingdom break up, significant damage to the economy or the destruction of the party itself rather than stay in the EU.

Asked about the YouGov findings, she said: “I think what’s important for the Conservative party is that we continue as a party and as a government in delivering on the values that have always underpinned what we as Conservatives believe in.

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“That’s about security and it’s about economic security through a balanced approach to the economy which is enabling us to end austerity.

“We are seeing employment at a record high, and it’s enabling us to bring our debt down and our deficit down. We also provide opportunity to people and you can see that, for example, in the new T-levels we’ve been introducing and giving people the freedom to be able to make decisions for themselves and the freedom to spend more of their own money.”

Ms May added: “I believe that Conservative party members, as with the majority of the public in the United Kingdom, want us to deliver on Brexit. I believe they want us to deliver not just in terms of leaving the EU, but the brighter future we believe we can have outside the European Union.

“That’s what I was working on and it’s what my successor will work on.”

And she said: “I’ve always said that I think it’s best for the United Kingdom to leave in an orderly way and that means leaving with a good deal. I believe I negotiated a good deal but parliament has not come to a majority supporting that.

“It will be up to my successor to find a way of delivering on the vote of the British people and doing that in a way which is in the national interest.”

Ms May came to Osaka with a message of support for international institutions and the spirit of “co-operation and compromise” which they embody. It was a message widely seen as being directed at US president Donald Trump.

But in her concluding address, she made clear it applies to Mr Johnson too.

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“This is my final G20 summit as prime minister of the United Kingdom,” she said.

“We have always understood that our success as a nation is tied to our collaboration with other countries and the relationships we build.