London's FTSE 100 rose 0.7 percent, outperforming European shares, and the FTSE 250 climbed 0.3 percent by 0840 GMT, on course to end 2019's first full trading week with the biggest gains since November.
Both indexes also hit their highest in more than a month.
Powell stressed again that the U.S. central bank can be patient in approving further rate hikes, while on the trade spat front, Treasury Secretary Steven Mnuchin said Chinese Vice Premier Liu He will "most likely" visit Washington later in January.
Shares on Wall Street notched their fifth consecutive session of gains following Powell's comments on Thursday, with Asian and European markets following suits.
But political tension deepened in Britain with Labour leader Jeremy Corbyn calling on lawmakers to help his opposition party "break the deadlock" over Brexit and support a motion of no confidence in the government to trigger an election.
Homebuilders, among the most sensitive to Brexit developments, shrugged off uncertainties and bounced after Bank of America Merrill Lynch upgraded the UK housebuilding sector to neutral.
Taylor Wimpey added 3.5 percent to lead FTSE 100 gainers, with Persimmon, Barratt Developments and Berkeley all advancing 1.3 to 2.6 percent.
"It seems at least possible, or even probable, that some sort of Brexit resolution is within sight and therefore the UK House Building sector may see some relief," BAML analysts wrote.
Energy shares were the biggest boost to the main index, climbing to their highest in a month as crude prices eyed solid weekly gains.
Airline Flybe plummeted as much as 90 percent to a life low of 1.7 pence after a heavily discounted 1 pence-per-share buyout offer from a consortium of Virgin Atlantic Ltd, Stobart and Cyrus.
Stobart jumped 5.6 percent to top mid-cap winners after the news.