The pound broke through the $1.35 mark for the first time in two months on Thursday amid hopes of progress in the Brexit negotiations.The jump followed reports the UK had offered to pay up to €50bn (£44bn) to settle its so-called EU divorce bill.The Times also reported on Thursday that the UK was close to a deal over the border with Northern Ireland and the Republic of Ireland.The dollar’s weakness in late New York trading exacerbated the pound’s gains.The pound was up 0.72% against the dollar at $1.3506. Against the euro, sterling rose 0.11% to €1.1334.”Pound traders continue to cheer the prospect of trade and transition deal talks following reports that the UK will cough up around €50bn for the Brexit divorce bill,” said Fiona Cincotta, Senior Market Analyst, at City Index. However, she added the “almighty rally” was also a “story of dollar weakness”. ‘Back with a thud’The dollar had been climbing as a result of hopes that President Donald Trump’s long-awaited tax reforms were making progress. But it “fell back to the ground with a thud” due to stagnant inflation in the US – which could make an interest rate rise less likely – and possible changes in Trump’s cabinet, Ms Cincotta.Elsewhere on the markets, the UK’s benchmark FTSE 100 share index was down 0.9% or 67 points at 7,326.67.Shares in Aviva ended the day 0.39% higher after the insurer increased its targets for growth and dividend payouts.On the FTSE 250 index, pub operator Marston’s saw its shares jump nearly 10% after it reported a rise in full-year profits and said it was “well positioned” for growth next year.But results from rival Greene King fell flat by contrast. Its shares dropped 3.7% after the brewer and pub owner reported an 8% fall in half-year profits and said trading conditions were likely to “toughen” in the next few years.