London’s FTSE 100 index of leading shares closed at a record high on Thursday, rising 0.3% to 7,556.24.
The rise of 22.43 points in the benchmark index took it above the previous high of 7,547.63, reached on 26 May this year.
However, the pound fell back after the EU’s chief negotiator said talks over Brexit were making little progress.
Michel Barnier said there was still “deadlock” over the so-called divorce bill, which he said was “disturbing”.
Sterling dropped in reaction to the news, with the pound down 0.39% against the dollar at $1.3173. It also fell 0.23% against the euro to €1.1122.
The index often benefits from a fall in sterling, as a weaker currency increases the value of companies’ overseas earnings when they are brought back to the UK and converted back into pounds.
“The UK stock market continues its winning streak despite concerns over economic performance and the unfolding Brexit process,” said Laith Khalaf, senior analyst at Hargreaves Lansdown.
“The question is whether the market’s strong run means it’s fit to burst.”
Sky was one of the biggest risers in the FTSE 100, up 1.4%, after the broadcaster reported a big rise in new customers.
Popular TV series such as Game of Thrones helped it to add 160,000 new customers in the first quarter of its financial year, up 51% on a year earlier.
In the FTSE 250, shares in Just Eat jumped 6.5% after the online takeaway ordering firm’s takeover bid for rival Hungryhouse was given provisional clearance.
The Competition and Markets Authority said the tie-up was “unlikely to result in competition concerns”.
It said the industry was “evolving rapidly”, with companies such as Deliveroo, Ubereats and Amazon all now entering the market.