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EXCLUSIVE-"Big progress" in Brexit talks leaves EU seeing trade deal closer - sources

* EU, UK moving “closer and closer to a deal” - EU sources

* EU welcomes nine of 10 UK proposals in area of social security

* Negotiations could run as late as mid-November - EU sources

* London eyes clarity by Oct.15, EU heads to assess next week (Adds UK comment, market reaction, senior EU official, detail)

BRUSSELS, Oct 6 (Reuters) - Britain and the EU are close to agreement on reciprocal social security rights for their citizens after Brexit, two diplomatic sources said, with one describing talks last week on an elusive trade deal as “one of the most positive so far”.

The European Union diplomats said Brussels was now gearing up to negotiate until as late as mid-November - rather than cutting talks off at the start of next month - to avoid a damaging “no-deal” scenario when Britain’s standstill transition with the bloc ends on Dec. 31.

There was no breakthrough at last week’s negotiating round on the three most contentious issues - fishing rights, fair competition guarantees and ways to settle disputes in the future - but the prospects of an overall accord looked much brighter.

“We seem to be getting closer and closer to a deal, even though the no-deal rhetoric in public might suggest the opposite,” said one of the two sources, both of whom were briefed in detail by the executive European Commission, which is negotiating with Britain on behalf of the 27-nation EU.

Sterling cut losses vs the euro on Tuesday after the report.

The sources spoke ahead of further talks in London starting on Wednesday with Britain, which formally left the EU in January after nearly half a century of membership.

At stake in the talks is an estimated trillion euros worth of bilateral trade. Investors and businesses are increasingly anxious about a split with no agreement to ensure the continuation of trade without tariffs or quotas.

Speaking separately this week, a senior EU official dealing with Brexit said the talks were “in a decisive period” and “not far away from the endgame”.

“I still hope and think that we can find an agreement,” the person said, but stressed that the EU and its industry must be ready for the most damaging economic split as well.

“TUNNEL” TALKS?

The 27 national leaders are due to meet in Brussels on Oct.15-16 to assess progress. If they decide a deal is in the making, they would authorise a final stretch of extremely secretive, make-or-break negotiations known as the “tunnel”.

The EU has so far said a deal must be finalised by the two sides’ negotiators - Michel Barnier and David Frost - by the end of October so that it leaves time for ratification by the European Parliament and some national parliaments in the bloc.

A new, mid-November target suggests hectic weeks ahead that would rattle financial markets if an eleventh-hour-deal is to be reached.

Asked to comment on the EU sources’ assessment on Tuesday, a UK official had no specific comment on social security coordination but said of trade talks overall: “A deal is possible but not certain.”

“Teams now need to work intensively to try and bridge the significant gaps that remain – on fisheries, the level playing field and governance. We remain fully committed to seeking to reach an agreement by 15 October.”

The two EU diplomats, speaking on condition of anonymity, said Britain had made welcome proposals on nine out of 10 areas related to protecting reciprocal social security rights for people moving between EU member states and the United Kingdom.

These proposals, which included benefits for accidents at work and death grants, were a basis to “very easily agree” a joint text on social security coordination, they said.

These protections could be critical for as many as 5 million people, whether it be a Briton in retirement in southern France or a German employed in London.

However, there was no agreement on a tenth area relating to family benefits. London wants EU citizens to pay a surcharge over five years for healthcare access for family members, while the EU says it should reciprocate the open access it offers.

Reporting and writing by Gabriela Baczynska, Additional reporting by Andreas Rinke in Berlin, Editing by John Chalmers and Gareth Jones

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