Visiting UK Prime Minister Boris Johnson on Monday said that a no-deal Brexit would be a "failure" that both the British and Irish governments would be responsible for but reiterated that it was essential for the country to leave the EU by October 31.

Johnson is in Dublin for his first face-to-face meeting with Taoiseach (Irish Prime Minister) Leo Varadkar since he entered Downing Street in July, the BBC reported.

While addressing the media here alongside Varadkar, Johnson said: "I have looked carefully at no-deal... Yes, we could do it, the UK could certainly get through it, but be in no doubt that the outcome would be a failure of statecraft for which we would all be responsible."

Johnson said that he understood the importance of the Irish backstop but added: "We need to find a way of ensuring that the UK is not kept locked in a backstop arrangement, while giving Ireland the assurance that it needs."

The backstop is part of the withdrawal agreement negotiated between Brussels and former Prime Minister Theresa May, which has been rejected by Parliament three times.

If implemented, it would see Northern Ireland staying aligned to some rules of the European Union single market, should the UK and the EU not agree a trade deal after Brexit.

However, Varadkar, while sincerely welcoming Johnson, said there was no such thing as a "clean break" between the UK and the EU, adding that the story of Brexit was no way nearly over.

"We both agree we have much to discuss, we accept the democratic and sovereign decisions to leave the EU," he said.

Varadkar added that "in the absence of agreed alternative arrangements, no backstop is no deal for us".

The Irish Prime Minister had invited Johnson to Dublin two months ago, shortly after he was assumed office, to discuss Brexit, the BBC reported.

The two leaders have very different views on how the deadlock should be resolved.

The Irish government maintains that the backstop was needed in any withdrawal agreement, because of decisions made by the UK.

But Johnson has said he will not sign up to a deal unless the backstop is removed, because it is "anti-democratic".