US Secretary of State Mike Pompeo has said the Trump administration will pursue a free-trade agreement with the United Kingdom as soon as possible after it leaves the European Union.

He made the remarks at a joint news conference in Washington with Britain's new Foreign Secretary Dominic Raab.

Mr Pompeo said the administration remains committed to respecting the British decision on Brexit, however it unfolds. He said they were aiming for an ambitious trade deal.

"However Brexit ultimately shakes out, we'll be on the doorstep hand-in-hand, ready to sign a new free trade agreement at the earliest possible time," Mr Pompeo said.

Speaking following a meeting in Washington, Mr Raab urged the EU to negotiate a new pact on Britain's departure to avoid a potentially calamitous "no-deal" Brexit.

He also said that the two sides agreed on the need for quick negotiations on a two-way deal after Brexit strands Britain outside the US-EU trade pact.

"America is our single largest bilateral trading partner. President Trump has made clear again that he wants an ambitious free trade agreement with UK, so I hope that we can make that happen as soon as possible after we leave the EU on the 31st of October," Mr Raab told reporters.

Mr Raab repeated British Prime Minister Boris Johnson's determination to leave the EU at the end of October whether or not the two sides set a new agreement governing post-Brexit relations.

Since Mr Johnson took office on 24 July promising to change the previously negotiated terms of the looming divorce, EU officials have refused to reopen talks.

"This government, this cabinet is absolutely resolved, determined to leave the EU by the end of October," Mr Raab said.

"There's a deal to be done. The PM has expressed that to our European partners," he added.

"But I think if the EU's position is that there can be no change to the withdrawal agreement, then that would be a choice that they've made, and that makes it very difficult to see how we can move a negotiation forward."

Speaking later from Mexico, which Mr Raab visited as part of his North America tour to strengthen Britain's economic ties with the region, he said the British government wanted to leave the European Union with a deal, but would do so without one if EU negotiators did not alter their stance.

"If the position from the EU is that the withdrawal agreement can't be changed - whether it's add-ons or subtractions - full stop, which is their position today, then let's face it, they will be taking the decision to see the UK leave on no-deal terms, and that's a responsibility they will have to bear." 

Asked about the backstop Mr Raab said that in its current form it was "undemocratic" and "will have to be removed", adding that the obvious alternative was to move towards an "operational backstop" that ensured that "any checks that are done wouldn't be at the border" but could be managed with "technology and goodwill and operational cooperation."

Yesterday, Minister for Finance Paschal Donohoe said he still believed a no-deal Brexit could be avoided, however he acknowledged that it was a risk that is growing.

He said it was important the UK, and the EU and Ireland, continue to engage with each other, but the Government would have to make a call as the end of October deadline approaches.

Additional Reporting Reuters