Boris Johnson has accepted that he has until the end of the week to save his Brexit plan, it is understood.

French president Emmanuel Macron told the prime minister on Sunday that the EU will decide within days whether an agreement is possible, as it will need to be signed off by leaders at next week’s European Council summit.

Responding, a senior government source said on Monday: “Everyone understands that we need to know by the end of this week where this is heading.

“It is understood by all sides what the time pressures are.”

It came as Dutch foreign minister Stef Blok called for “more realism and clarity” from the UK after a meeting with Brexit Secretary Stephen Barclay.

But Britain made clear it would refuse any demands to compromise on its customs proposals for Northern Ireland, one of the key issues standing in the way of a deal.

Under the so-called “two borders, four years” scheme put forward by Johnson, Northern Ireland would leave the European customs territory along with the rest of the UK, requiring some checks on goods leaving and entering the six counties.

When asked whether the UK would compromise and allow Northern Ireland to remain in the same customs territory as Ireland and the EU in order to get a deal, Number 10 ruled it out.

The PM’s spokesman said: “The prime minister set out in his letter on Wednesday to Jean-Claude Juncker that we believed this provided a broad landing zone and that we were willing to engage on further discussions of our proposals.

“But if your question is are we prepared for Northern Ireland to be in a different customs union territory to the United Kingdom, the answer is a very firm no.”

Johnson was continuing his round of telephone diplomacy on Monday, holding talks with the leaders of Sweden, Denmark and Poland.

There are currently no plans for the PM to travel to Europe to meet other leaders, although face-to-face talks with Leo Varadkar may be in the offing later this week.

On a visit to Watford General Hospital, Johnson urged the EU to make concessions.

“We’ve gone a long way. We’re talking about keeping Northern Ireland in alignment with Ireland by consent, whether over agri-foods or over industrial products and standards,” the PM said.

“Now that’s a big concession by the UK. The issue is what is the EU’s objections to that? What’s their suggestions? Where are they coming from? We haven’t really heard the detail from them about what they think the problems are.

“It’s time for us to get together and really thrash this thing out. And I think we can.”