Some Conservatives would rather see Jeremy Corbyn become prime minister than let Brexit go ahead, Lord Heseltine has claimed.

The pro-EU former Tory deputy prime minister said on Friday that Theresa May had “no majority” for the sort of Brexit, outside the customs union and single market, that she wanted.

“There are Conservatives who feel so strongly about the European issue that they would rather risk the short-term damage of a Corbyn government, and let’s not under-estimate that, than to see Britain make this calamitous mistake of leaving Europe,” he told BBC Radio 4′s Today programme.

“There are an increasing number of people, particularly the young people, and by that I mean under 40, who today think that Corbyn is an alternative they can live with.”

Corbyn has committed Labour to keeping the UK inside a customs union with the EU after Brexit.

Lord Heseltine praised the “very brave” Conservative MPs who have threatened to vote with Labour in order to defeat the government when there is a Commons vote on the customs union.

His comments come as May prepared to use a speech on Friday afternoon to set out her vision of the future economic relationship between the UK and EU.

Ahead of the prime minister’s speech, Transport Secretary Chris Grayling acknowledged the UK will not be able to “have everything that we might like” from the EU after Brexit.

He predicted that some of the strong rhetoric around the kind of relationship the UK would be able to have with the EU after Brexit would “come out in the wash” during the course of the negotiation.

“The Prime Minister will recognise that it is not about cherry-picking, we can’t have everything that we might like to have because we are leaving,” he said.

Labour’s Shadow Brexit Secretary Kier Starmer said this morning that May was right to reject the EU’s proposal that Northern Ireland effectively remain in the single market and customs union after Brexit while the rest of the UK leaves.

The prime minister said the plan would undermine the “constitutional integrity of the UK” as it would place a border between Northern Ireland and the rest of the UK.

Starmer said: “Theresa May is absolutely right about that. I don’t see that any prime minister could agree to it.”

But he said the only reason Brussels had made the suggestion was because there was an “absence” of any plan from the British government.

“It’s simply not a road that we could go down, but that really ramps up the pressure on her to say what then is the answer,” he said.

Starmer said Labour had gone “a long way” to providing an answer by arguing for the whole of the UK to stay in the customs union.

In her speech, May will tell EU leaders she wants the “deepest and broadest possible” trade agreement with the bloc as she seeks to lay the ground for the next phase of the Brexit negotiations.

The prime minister will set out her vision of a free trade deal based on maintaining “high standards” of regulation, while managing any future divergence by the UK from existing EU rules.

While she will say that she wants Britain to have the freedom to strike trade deals around the world, it should be possible to agree a relationship with the EU where they continue to “support each other’s interests”.

At the same time she will stress that any agreement must respect the outcome of the 2016 referendum vote to take back control of “our borders, laws and money”.

After her angry rejection on Wednesday of a draft EU proposal for Northern Ireland to remain in the single market and the customs union – unlike the rest of the UK – to avoid the return of hard border with the Republic, she will say it must also preserve the UK’s “union of nations”.