European Council president Donald Tusk hinted at a frosty meeting with Theresa May as he told the British prime minister he is "not happy" with her Brexit "red line".

Mr Tusk met with Mrs May at 10 Downing Street today, despite snowy conditions in London.

Their talks came a day after Mrs May rejected EU proposals to establish a "common regulatory area" between the bloc and Northern Ireland after Brexit.

As he sat alongside Mrs May in Number 10, in front of photographers, Mr Tusk told the British PM: "I'm absolutely sure that after your so-called red line... well I'm not happy with it, you know, but of course, but it's natural that you have maybe different point of views when it comes to the essence of Brexit.

"Anyway, after your decision on no customs union and no single market it's some kind of breakthrough and we can start our substantive negotiations immediately."

Mr Tusk also apologised for his lateness to the meeting, joking that his "transport was not frictionless" as the UK is gripped by freezing temperatures.

Earlier in the day, the European Council President had dismissed Mrs May's hopes for post-Brexit trade between the UK and EU to be "as frictionless as possible".

Their talks also touched on the planned Brexit transition period and Northern Ireland, while Mr Tusk confirmed all other 27 EU member states were giving their "full support" to the bloc's chief Brexit negotiator Michel Barnier, the source added.

'Friction is an inevitable side effect'

On Thursday morning, in a speech in Brussels, Mr Tusk said the EU acknowledged Britain's "red lines" to quit the bloc's single market and customs union "without enthusiasm and without satisfaction".

But he added the EU would "treat them seriously with all their consequences".

"There can be no frictionless trade outside of the customs union and the single market," he said.

"Friction is an inevitable side effect of Brexit. By nature."

He also revealed he would be asking Mrs May for "a better idea" than the EU plan she has rejected for avoiding a hard border on the island of Ireland.

"Until now, no-one has come up with anything wiser than that," Mr Tusk said.

On Wednesday, Mrs May insisted "no UK prime minister could ever agree" to a plan for a "common regulatory area" between the EU and Northern Ireland, included in a 118-page document set out by Mr Barnier on Wednesday morning.

The proposal would see such an area established in the event a EU-UK agreement on a future relationship fails to prevent a hard border on the island of Ireland.

Under the plan, Northern Ireland would remain an effective part of the EU's customs union, align with the EU on VAT, abide by Brussels rules on state aid, and remain under the jurisdiction of the European Court of Justice.

It has also sparked angry accusations that Brussels is trying to "annex" Northern Ireland.

On Friday, Mrs May will flesh out the government's position on the future EU-UK trade relationship ahead of the second phase of Brexit negotiations.

Next week, Mr Tusk will set out the EU27's own guidelines on a post-Brexit trade agreement.