The action, although widely expected, prompted the pound to fall by 1.5% against the dollar.
The FTSE 100 closed up 105 points at 6,740.16, higher than the same day last year.
The pound was down 1.5% against the dollar at $1.3120 and was down 1.3% against the euro at 1.1799 euro.
"We got a Goldilocks dose of stimulus from the Bank of England today, not too dovish and certainly not too hawkish," said Neil Wilson, markets analysts at ETX Capital.
"The inclusion of corporate bonds in the QE programme is noteworthy. It’s going to deliver another sugar rush for the FTSE 100 and it’s no doubt going to spur additional borrowing by investment-grade companies who can then use the funds to finance share buy backs," he said.
"The weaker pound is also good news for the blue chip index, as earnings predominantly come from abroad," Mr Wilson added.
Another analyst pointed out that both the FTSE 100 and the pound have been stuck in a range for weeks.
"What is interesting... is that this still leaves both instruments [FTSE 100 and pound/dollar] within the same trading brackets they have been bouncing around for the last few weeks, reflecting, perhaps, the extent to which today’s action from Carney and co. was expected," said Connor Campbell, financial analyst at SpreadEx.
"It also doesn’t necessarily give either the UK index or sterling any fresh direction for the coming weeks and months, leaving both at the mercy of the next wave of Brexit-impacted data," he said.
The biggest loser on London’s leading index was pharmaceutical company Hikma. It plunged by 17% after a late release on Wednesday, warning profit at its generic drugs unit would fall this year.
Insurance giant Aviva was a winner, rising 7% after announcing a 13% half-year operating profit rise.
Outsourcing company Serco was up 10% after it raised its 2016 profit forecast for the second time this year.
It voiced a positive note on Brexit, saying it could bring opportunities - as well as costs.
Standard Chartered Bank saw another good share price rise of 5%, building on Wednesday’s 4.2% gain on results.