Former chancellor George Osborne has called on Theresa May to seek "the closest possible new ties" with European states as she negotiates Britain's exit from the EU.
And he urged the new Prime Minister to stick to commitments entered into by David Cameron to spend 2% of national income on defence and 0.7% on international aid, and to press ahead with his own Northern Powerhouse project to promote economic growth in the north of England.
Mr Osborne, who was sacked from the Cabinet when Mrs May took office last Wednesday, admitted he had "put everything on the line" by backing Remain so strongly in the EU referendum.
But he insisted that he did not regret his stance on the EU and would not back away from any of the dire warnings he made about the damage Brexit would do to the UK's prospects.
Delivering the annual Margaret Thatcher Lecture to the Centre for Policy Studies at London's Guildhall, Mr Osborne said: "As you all know, I fought hard - as hard as I could - for a different outcome to the referendum we have just held on our membership of the EU.
"I didn't do it by half-measures; I couldn't on an issue like that. I put everything on the line, and don't regret for a moment that I did.
"But while I don't resile from any of the concerns that I expressed in advance of that vote, nor do I intend to re-run the arguments now the vote has passed."
And he added: "Tonight, and in the future, Theresa May and the new team she has assembled will have my support.
"She has the strength and the integrity to do the job, as she faces up to the great challenge that lies ahead."
Mr Osborne said there was no-one he would rather see succeed him at the Treasury than the new Chancellor Philip Hammond, and offered him his "full backing".
But he set out the priorities which he believed the new Government should follow as it negotiates its new relationship with Europe. The former Chancellor said: "As we negotiate our exit from the EU, I hope we seek the closest possible new ties with our European neighbours.
"They are, on the economy and on security, our friends, not our foes.
"I hope we reach out to build stronger economic and trading ties now with our old allies like the United States, and our new partners like China.
"I hope we maintain the 2% of national income I committed us to spend on defence; and the 0.7% we were able to spend on international development - it makes us unique among the major nations, with world-besting hard power and world-changing soft power, too.
"A Britain strong at home, but also strong in the world."
Mr Osborne welcomed the "One Nation" message delivered by Mrs May in her speech on the doorstep of 10 Downing Street last week, and said that this should involve continued backing for the Northern Powerhouse.
"As Home Secretary, Theresa May has often spoken out against discrimination and I was hugely encouraged to hear her on the steps of Downing Street last week speaking about her One Nation vision for her government," he said.
"She understands that One Nation isn't possible if parts of our country feel disconnected from its economic success and disenfranchised from a stake in our society.
"The regional variation in the referendum result revealed how much more work we have to do, especially in the North and Midlands.
"Many of the issues I pursued in government will now be for a new set of ministers to pick up. But I remain passionately committed to the Northern Powerhouse - and I won't let go of that."