The pound rose above $1.32 as markets welcomed the removal of uncertainty from the Conservatives Party's leadership contest, with Theresa May set to be the new prime minister.
The FTSE 100 share index hit fresh 11-month highs before falling back and closing scarcely changed at 6,680.69, that is a slight fall of 2.17 points or 0.03%.
The more UK-focused FTSE 250 index rose 68.75 points, or 0.4%, to 16,775.14.
The property sector - which saw a steep sell-off immediately after the Brexit vote - received a boost from Galliford Try. The housebuilder said it still expected full-year profits to be in line with expectations sending its shares up 8.5%.
"Theresa May's virtual 'coronation' as prime minister has delivered a boost to the pound as the clouds of uncertainty following the Brexit vote start to disperse," said Neil Wilson, markets analyst at ETX Capital.
"The leadership question has been settled and two months earlier than markets had been anticipating. This is feeding into strong bids for sterling and property stocks as investors eye potential bargains."
The removal of uncertainty at the top of the Conservative Party also provided a boost to sterling.
The rise came despite evidence to MPs on the Treasury Select Committee on Tuesday from the Governor of the Bank of England.
Mark Carney indicated that the Bank, whose monetary policy committee meets on Thursday, was ready to provide more stimulus to cushion the British economy.
"We see more downside for the pound both on Thursday and the months ahead," said Josh O'Byrne, Citi currency strategist in London.