A no-deal Brexit will not enable the UK to leapfrog unresolved issues to negotiate a free trade agreement with the EU, the Taoiseach has warned.

Leo Varadkar said in the wake of a no-deal, talks on a future trading relationship would still not begin until matters in the current withdrawal deal - such as citizens' rights, the financial settlement and the Irish border - were resolved.

On a visit to Northern Ireland, the Taoiseach said a no-deal was not inevitable and he was not being "fatalistic" about its likelihood.

But he said the risk of a disorderly exit was increasing as the clock ticked towards 31 October.

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After touring Hillsborough Castle in Co Down, the Queen's official residence in the region, Mr Varadkar said the Brexit process would not end on 31 October, even if there is no deal.

"There are people who have perhaps become frustrated with the Brexit process and they are almost saying to themselves 'you know, at least if we have no deal on the 31st of October it's all over and it's all done'," he said.

"What I am saying is it doesn't end on the 31st of October, if we have no deal we are going to have to talk and the first things on the agenda are going to be citizens' rights, the financial settlement and the solution to the Irish border, before we even start to talk about a free trade agreement."

He added: "If there is a deal, we are going to enter into several years of negotiations on a new free trade agreement with the UK and a new economic and security partnership."

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Mr Varadkar continued: "So, Brexit isn't a storm that we weather or a severe weather event that we prepare for, it is a permanent change in relations between the European Union, including Ireland, and the United Kingdom. I think that needs to be borne in mind."

The Taoiseach reiterated the EU position that the Withdrawal Agreement was not open for renegotiation.

But he insisted there was scope to offer clarifications on the deal and make changes to the Political Declaration on the future relationship.

"I don't accept it's unavoidable," he said of the prospects of a no-deal.

"There are many ways by which a no-deal can be avoided. Either by the ratification of the Withdrawal Agreement, a further extension, or revocation of Article 50.

"So, there are a number of ways that a no-deal can be avoided on the 31st of October. I am certainly not fatalistic about that."

Earlier, the Taoiseach attended an Ireland Funds Young Leadership series event at a cross-community project in north Belfast funded by the EU and took part in the Leaders' Debate at the West Belfast Festival.

Meanwhile, Minister for Finance Paschal Donohoe met his counterpart, Sajid Javid, in London for talks on Brexit.

It was the pair's first meeting since Mr Javid was appointed Chancellor of the Exchequer by British Prime Minister Boris Johnson. 

"Most of our discussion was around how we would avoid a hard border and how we will avoid the consequence(s) of a hard border on the island of Ireland and what a hard border would mean for Northern Ireland," said Mr Donohoe after the talks.

He said this is where one of the points of divergence is.

The minister added: "From our point of view, we believe the most effective way of ensuring we do not have a return to a hard border is the ratification of the Withdrawal Agreement, including the backstop.

"The chancellor outlined his views regarding why he did not believe the backstop could play a part in the future Withdrawal Agreement.

"The chancellor reaffirmed what Prime Minister Johnson has said in relation to the Withdrawal Agreement and in relation to their view that the backstop cannot form part of that Withdrawal Agreement."

Mr Donohoe was in London with the upcoming Budget on 8 October at the forefront of his mind.

The minister has prepared two Budgets, one for an orderly Brexit and the second for a disorderly scenario.

A decision on which case will become the central scenario for planning October's budget is due to be taken in September.

Elsewhere, the deputy leader of the DUP has called on the Irish Government and the EU to engage with Britain on finding an alternative to the backstop.

Nigel Dodds said: "It is positive that there is acceptance amongst the EU27, as well as clear statements from our own government that there will be no hard border, even in a no-deal scenario. All of which means the fuss about a backstop is unnecessary.

"With the clock counting down towards 31 October, it is time for Dublin and Brussels to engage constructively and work for a deal which respects the constitutional and economic integrity of the United Kingdom."

Discussions between the UK and the EU, including Ireland, are currently deadlocked over the backstop.

Additional reporting: Aisling Kenny