The internationally-exposed FTSE 100 index was up 0.7 percent at 6,634.55 points by 0706 GMT after rising up to 6,637.19, a level last seen before the summer swoon across global markets last August.
Since the referendum on June 23, Britain's FTSE 100 index has gained two percent as of Wednesday afternoons trading.
According to analyst Joshua Mahony of IG, markets expect a 75 percent chance of the key interest rate being cut from 0.5 percent to 0.25 percent.
The FTSE 100 built on gains made on Friday after a positive USA jobs report, with house builders among the biggest risers, rallying from "Brexit" lows as investors anticipated lower mortgage costs from a cut in rates.
'Equity markets continue to ride north helped by a United States jobs report seen to quell fears about a USA economic downturn and jobs market weakness, without fuelling fears about a Fed rate hike waiting in the wings, ' said Mike van Dulken, head of research at Accendo Markets.
But sterling later headed back down below that mark - possibly reflecting the fact that markets are more focused on events at the Bank of England this week than in Whitehall.
London's top flight index rallied towards the closing bell as it was confirmed that Theresa May would be in post as prime minister by Wednesday after rival candidate Andrea Leadsom dropped out of the race.
The pound, which was down below $1.29 against the Dollars rebounded as reports circulated that Leadsom will not contest.
The pound stepped up 0.3% against the euro to 1.176. Some more quantitative easing is also on the way and it is likely that stocks will remain well-supported, if volatile.
Khalaf added: "Overall the FTSE has definitely proved resilient in the face of all the uncertainty created by the Brexit vote, though that really is testament to the worldwide make-up of the index, and the long-standing faith in central bankers to come to the rescue by turning on the printing presses".
Elsewhere, the FTSE 250 - which paints a more accurate picture of United Kingdom investor sentiment as the vast majority of firms in the index are UK-based - rallied massively on the day, up by 3.23%.
The beneficiaries of London stock market rally in FTSE 100 were mainly property companies whose shares were hit by Brexit vote.
Barratt Developments (BDEV) jumped 7.8% to £14.64, Berkeley (BKGH) was up 7.6% at £26.80, Taylor Wimpey (TW) rose 7% to 140.7p and Persimmon (PSN) added 6.5% to £15.12.
The London stock rally that pushed FTSE 100 was a relief for the property companies.