The pound has jumped to its highest level in five months on reports the two sides in the Brexit talks are inching towards a draft deal.
Shares in banks and housebuilders also soared as optimism about a breakthrough buoyed companies with a UK focus.
It was hoped that a preliminary deal might be reached on Tuesday, ready to go before a summit on Thursday.
Sterling rose 1.5% on the dollar to $1.28, and by a similar amount against the euro to 86.3 pence.
On the FTSE 100, shares with a big exposure to the health of the UK economy rose sharply. Builders Barratt Developments and British Land were up about 6%, and Lloyds Banking Group and Royal Bank of Scotland rose more than 5%. Next, ITV and Ocado were also big risers.
“A deal between the UK and EU was 60% in the price [of sterling] and now we stand to see if the remaining 40% come into play,” said Stephen Gallo, European head of foreign exchange at BMO.
Morten Lund, a senior forex strategist at Nordea, added: “The reaction from the markets shows they want to get this deal over and they are ready to push the button at the slightest sign of a deal.”
But he said he was “a bit more sceptical about the outcome” given how little time remained to negotiate and the difficulties of getting a deal through the British Parliament. The UK is due to leave the EU on 31 October.
Shares and the pound jumped last week on growing optimism of a deal, only to slip amid signals from Brussels that the negotiations still had a long way to go.
But on Tuesday, Brussels’ chief Brexit negotiator Michel Barnier sparked another rise on the markets when he said it was “high time to turn good intentions [into] a legal text”.
Irish PM Leo Varadkar said talks were “moving in the right direction”. Boris Johnson has spoken to France’s Emmanuel Macron and the BBC understands the two men agreed there was “positive momentum”, although “many hurdles” must still be overcome.
The FTSE 250 of UK mid-cap stocks rose and European equity benchmarks extended their gains on the news.
“The more uncertainty you remove, the better for investors. If the [UK] prime minister and the EU were now to agree a deal, then the market would take that positively,” said Edmund Shing, global head of equity derivatives strategy at BNP Paribas.