George Osborne has warned Theresa May against pursuing a “hard Brexit” that would see the UK drifting away from cooperation with the rest of Europe.

The former chancellor made the remarks at a speech in Chicago, in a sign that he intends to continue to play a role in the political debate about leaving the EU, despite departing the government at the same time as David Cameron.

Osborne, who campaigned strongly to remain, argued that it was unwise for politicians to claim the UK had a stronger hand in negotiations than the EU.

“I find some of the take-it-or-leave-it bravado we hear from those who assume Europe has no option but to give us everything we want more than a little naive,” he told the Chicago Council on Global Affairs.

“We need to be realistic that this is a two-way relationship – that Britain cannot expect to maintain all the benefits that came from EU membership without incurring any of the costs or the obligations.”

He urged May’s government to “resist the false logic that leads from exiting the EU to exiting all forms of European cooperation – and that values the dangerous purity of splendid isolation over the practical necessity of cooperation in the real world”.

“Brexit won a majority. Hard Brexit did not,” Osborne said.

The former chancellor also predicted that there would be no serious progress in negotiations with the EU until after the French and German elections next year.

“It is highly unlikely that the rest of Europe will be in any position to conduct serious negotiations until the autumn of next year.

“My experience of six years of European negotiations is that nothing serious happens until the French and, especially, the German governments take a view – and both countries will be preoccupied with their own domestic elections for much of next year.”

The Tory MP Dominic Grieve, a former attorney general and leading supporter of the Open Britain campaign group, said: “George Osborne is absolutely right that a hard Brexit has no mandate and would be no answer to the problems Britain faces.

“In fact, it would put jobs and livelihoods at risk by erecting new barriers to trade with Europe. As he said, being close to Europe despite the Brexit vote is vital for Britain’s future.

“Our economic future depends on membership of the single market, while cooperation with Europe on security is crucial in the fight against terrorism and organised crime.”

It was Osborne’s first major speech since he lost his job when May took over from Cameron as prime minister in July. Since then, she has set about unravelling key aspects of Osborne’s economic policy and overturning central tenets of Cameron’s premiership, such as his opposition to bringing back grammar schools.

Osborne indicated in a BBC Radio 4 interview last week that he would stay on the political scene but he gave only a lukewarm endorsement of May’s premiership.

May is facing competing pressures when it comes to carrying out negotiations with the EU. She has said she wants a bespoke deal for Britain that preserves free trade at the same time as curbing free movement for EU citizens to come to Britain.

Some of the most hardline Eurosceptics would like her to be prepared to walk away from the single market and close trade cooperation if the EU does not concede to strict controls on immigration.