Brexit negotiations with the EU will “go to the wire”, Jeremy Hunt has said, just hours after Theresa May delivered a major speech designed to help talks progress.

The Health Secretary dismissed suggestions the speech lacked detail but admitted it would be “very difficult” for the EU to agree to the proposals put forward by the Prime Minister.

The negative response to Ms May’s speech from some European leaders was “inevitable”, he said.

The Prime Minister used the speech at Mansion House in London to outline a future UK-EU relationship that she said would enable close trading links despite Britain leaving the single market and customs union.

She confirmed the UK will seek to remain a member of several European agencies and will maintain similar regulations to the EU in order to enable “frictionless trade”, but with the option of diverging at a later date if it chooses to do so.

The speech was welcomed by many in her own party, including leading Brexiteer and Remainer MPs, but criticised by some EU leaders for having failed to provide detail on key issues.

Responding to those claims, Mr Hunt told the BBC Today programme: “It’s always going to be inevitable in these kind of situations that people will say it’s not enough detail, because this is a negotiation.

“You’re hardly going to get Europeans saying, ‘Fantastic, thank you, you’ve solved all my worries, let’s sign along the dotted line’.

“It’s going to be a negotiation and I’m sure it will go to the wire as these things always do.”

Guy Verhofstadt, the European Parliament’s Brexit lead, had earlier said the Prime Minister had failed to “move beyond vague aspirations” and that he hoped “serious proposals have been put in the post”.

“While I welcome the call for a deep and special partnership, this cannot be achieved by putting a few extra cherries on the Brexit cake,” he said.

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Mr Hunt denied Ms May’s speech amounted to an admission that Brexit will not be as easy to deliver as Tory ministers had previously claimed.

“I don’t think anyone ever said that it wasn’t going to be incredibly complex and incredibly challenging,” he said, adding that trying to negotiate a trade deal with the EU is a “complicated venture”.

Liam Fox, the International Trade Secretary, has previously claimed a deal with the EU would be “one of the easiest in human history”, while Brexit Secretary David Davis predicted an agreement would be reached “quickly”.

Mr Hunt said Ms May was right to state that compromise will be necessary, and admitted some of the UK’s aims will be difficult for the EU to accept.

“We have to accept that both sides are going to have to make compromises,” he said.

“What we want to do is have a close economic partnership, which allows the British economy to thrive, but also full control of our laws.

“That is very difficult for European countries to agree to because they want us to pay some kind of price for the fact that we decided to leave the EU.”

Theresa May: We want to negotiate remaining a member of the European Medicines Agency

Expanding on Ms May’s vision, he admitted the UK will lose some of its market access after Brexit but insisted “frictionless trade” could be achieved through a “voluntary” alignment of regulations with the EU.

The Prime Minister’s speech received a warm response from many Conservatives, with pro-EU MPs such as Nicky Morgan and Sarah Wollaston saying it had provided much-needed detail on the UK’s plans.

Brexiteers, meanwhile, welcomed the confirmation that the UK will be leaving the single market, customs union and jurisdiction of the European Court of Justice.

Mr Hunt said the Tories were more united after Ms May’s speech.

“As we think about how we set up a new partnership with Europe, there are very entrenched positions on both sides,” he said.

“Actually what the Prime Minister is doing here is bringing those sides together. I don’t think at the start of this week any of us would have thought there could have been a speech that is welcomed both by Jacob Rees-Mogg on one side and by Nicky Morgan on the other.