* UK, EU to hold intense negotiations
* Pound, UK-focused stocks surge
* Oct. 31 deadline nears
* Irish border key to deal
* Parliament could still stand in Johnson's way (Adds DUP, Farage response)
By Gabriela Baczynska and Jonas Ekblom
BRUSSELS, Oct 11 (Reuters) - The European Union agreed on Friday to enter intense talks with Britain to try to break the deadlock over Brexit, lifting financial markets with a sign that a deal could be done before the Halloween deadline.
A flurry of activity has brought the fraught bargaining process to a new level as Britain's scheduled departure date of Oct. 31 grows ever closer, but it is still uncertain whether the two sides can make a breakthrough before then.
The move came at the end of a tumultuous week which started with a public row between London and Brussels.
By Thursday British Prime Minister Boris Johnson and his Irish counterpart Leo Varadkar said they had found "a pathway" to a possible deal, and by Friday some officials were expressing guarded optimism.
"I think both of us can see a pathway to a deal, but that doesn't mean it's a done deal," Johnson said on Friday. "There's a way to go, it's important now our negotiators on both sides get into proper talks about how to sort this thing out."
Ireland is crucial if a deal is to be done to avert a potentially disorderly Brexit that would hurt global growth, roil financial markets and could even split the United Kingdom.
Dublin will have to consent to any solution to the toughest problem of all: how to prevent the British province of Northern Ireland from becoming a backdoor into the EU's markets without having border controls.
A diplomat and an EU official said EU negotiator Michel Barnier had told member states that Britain had changed its position and now accepted that its proposed replacement of the so-called "backstop" cannot involve a customs border between EU member Ireland and Northern Ireland.
The backstop is an insurance policy that was designed to ensure no customs or regulatory checks on the border between Ireland and Northern Ireland after Brexit.
Separately, two senior EU diplomats told Reuters the possible solution could include two elements: keeping Northern Ireland inside the UK's customs regime while also carrying out any customs and regulatory checks together.
Under a recent UK proposal, the regulatory border would run down the Irish Sea between Northern Ireland and Britain. The sources said they understood that customs checks could be carried out there as well under the plan now under discussion.
But in a sign of the precarious nature of the talks, the Democratic Unionist Party (DUP), the small Northern Irish party which supports Johnson's government in parliament, warned it would only compromise so far.
"The DUP has always indicated that the United Kingdom must leave the EU as one nation and in so doing that no barriers to trade are erected within the UK," leader Arlene Foster said, without rejecting the proposal outright.
Johnson declined to give a direct answer when asked by reporters if Northern Ireland would leave the EU customs union.
"LIKE CLIMBING A MOUNTAIN"
Barnier, who held "constructive" talks with Britain's Brexit minister Stephen Barclay on Friday, said the Europeans would take stock again on Monday.
Barnier told reporters as he left his meeting with Barclay: "Brexit is like climbing a mountain. We need vigilance, determination and patience."
Other EU officials agreed the challenge remained huge.
One European diplomat indicated to Reuters that there was not too much hope on the EU side that a divorce deal could be sealed before the end of the month.
"It's a tunnel with a very small light at the end of it," a second diplomat said.
In Paris, French President Emmanuel Macron, asked by a Reuters reporter if there was a "glimmer of hope" regarding a Brexit agreement, replied: "Let us wait for the next few hours."
EU ministers convene in Luxembourg on Tuesday for a last meeting before an EU summit next Thursday and Friday.
Johnson said there was still a long way to go and if negotiators fail to reach agreement "then we have to be ready, as this country is and will be, to come out with no deal if we absolutely have to".
To get a deal done, he must also sell any deal to the British parliament, which he suspended unlawfully last month and where his Conservative Party has no majority.
Johnson, the face of the 2016 Brexit referendum campaign, insists the country will leave on Oct. 31 with or without an agreement but he has not explained how that will be possible without defying parliament, which passed a law saying Britain cannot leave the bloc without a deal.
Nigel Farage, the leader of the Brexit Party, showed the challenge Johnson will face if he tries to move too far to accommodate Brussels.
"I don't know what Boris Johnson has given away, but he sounds very defensive," he said on Twitter. "Let us hope that this is not a surrender."
The Brexit issue has deeply polarised the country and many businesses fear they will be hit badly by a disorderly break with the EU.
Big investment banks said on Friday they had become more optimistic on the prospects for a deal, pushing sterling to a three-month high, taking its rally since Thursday to more than 3%, its biggest two-day gain since mid-June 2016, before the Brexit referendum.
Shares in companies exposed to Britain's economy also surged, with Royal Bank of Scotland joining housebuilders such as Persimmon, Barrett and Taylor Wimpey in rising about 10%.
The yield on 10-year British government bonds was on track for its biggest three-day rise since 2017.
(Additional reporting by Guy Faulconbridge, Costas Pitas, Elizabeth Howcroft, Josephine Mason and David Milliken in London, Amanda Ferguson in Belfast and Michel Rose in Paris, Writing by Angus MacSwan and Kate Holton Editing by Jon Boyle and Gareth Jones)