BRUSSELS (Reuters) - Britain and the EU are closer 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 in last week’s negotiations on the three most contentious issues - fisheries, fair competition guarantees and ways to settle future disputes - but the prospects of an overall accord looked 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 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, holding near to $1.30. The sources spoke ahead of further talks on Wednesday-Friday in London with Britain, which left the EU in January after nearly half a century of membership. At stake 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 EU industries must be ready for the most damaging economic split as well. A deputy head at the Commission said separately on Tuesday the EU wanted a deal with Britain, but that time was running out and the sides risked failing to get one by the end of the year. “TUNNEL” TALKS? Prime Minister Boris Johnson’s spokesman also said on Tuesday Britain needed to know by Oct.15 if there was going to be a deal because businesses need to prepare. The 27 national leaders are due to assess progress when they meet in Brussels on Oct.15-16. 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 end of October to leave time for ratification by the European Parliament and some national parliaments in the bloc. A new, mid-November target suggests hectic weeks ahead would rattle financial markets if an eleventh-hour-deal is to be reached. Brussels insists, however, it will not implement any new deal without Britain rowing back on proposed new domestic legislation that would violate London’s earlier divorce settlement with the EU. Asked to comment on the EU sources’ assessment on Tuesday, a UK official said: “A deal is possible but not certain... 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 of protecting 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 family benefits. London wants EU citizens to pay a surcharge over five years for healthcare access for family members, while the bloc says Britain should reciprocate the open access it offers. The UK official said good progress had been made on social benefits but that outstanding issues were also significant, adding that London would not change its stance on the health surcharge or on access to family benefits.