Britain and the EU agreed on Thursday to hold more talks to try to avoid a no-deal Brexit, after a "robust" meeting between Prime Minister Theresa May and European Commission chief Jean-Claude Juncker.

A joint statement issued after the talks in Brussels said Juncker had again warned that November's withdrawal agreement could not be renegotiated -- after May came hoping to persuade Brussels to change the so-called "backstop" clause for the Irish border.

But Juncker expressed only his "openness to add wording" to a parallel political declaration laying out ambitions for future EU-UK ties if London wants to seek a "more ambitious" closer relationship after Brexit.

After his own talks with May, EU President Donald Tusk warned there was "no breakthrough in sight", though the British leader said she had seen willingness from Brussels to find a deal.

"Prime Minister May did not offer any new concrete proposals on the way forward," an EU official told AFP after May's meeting with Tusk.

Talk has been growing that Britain may have to delay Brexit to give enough time to get the necessary legislation through parliament, but May vowed once again to bring Britain out of the bloc on schedule on March 29.

"I'm going to deliver Brexit, I'm going to deliver it on time. That's what I'm going to do for the British public. I'll be negotiating hard in the coming days to do just that," she said.

The EU official said Tusk had asked May about the timeline for British officials and parliament to ratify and implement a deal, but received "no clear answers."

And Tusk also, the official said, suggested to May that she study a Brexit plan laid out earlier in the day by British opposition Labour leader Jeremy Corbyn, which "might be a promising way out of the impasse." May did not respond.

In a sharp reminder of the urgency of finding a solution before Brexit day, Bank of England governor Mark Carney warned that Britain's economy was "not yet prepared" for a no-deal departure.