The FTSE 100 was up 0.3 percent by 0927 GMT while the domestically-focused FTSE 250 gave up initial gains and was down 0.1 percent, underperforming its European peers.
British lawmakers appeared set to reject May's plan, and a heavy defeat could force her to delay Britain's scheduled departure from the EU on March 29. It could also open up other options ranging from a second referendum to leaving the EU with no deal.
"Of course, we could get a situation where the vote gets passed, but given the polling numbers that looks about as likely as finding a unicorn," said CMC Markets analyst Michael Hewson.
In a last-ditch effort, May urged lawmakers on Monday to take a second look at her deal and warned parliament it risked the break-up of the United Kingdom if it voted against the agreement.
"There may be some marginally relevant news flow, but the big picture is just vast uncertainty," said CityIndex market analyst Ken Odeluga.
Raymond James analyst Chris Bailey said "the market is still a slave to Brexit newsflow and clearly multiple future scenarios exist, albeit that a 'soft' or delayed Brexit has become much more likely than the more apocalyptic 'no-deal' scenario."
Banks and oil majors BP and Shell led the charge on the main index after China signalled more growth-boosting steps and oil prices rose amid supply cuts.
Asia-focused bank HSBC was the biggest boost to the FTSE 100.
Homebuilders, among the most exposed to Brexit uncertainty, fell to their lowest in nearly two weeks and cast a shadow over a bright update from Britain's second-biggest housebuilder Persimmon.
Gambling firms fell after the U.S. Department of Justice hinted at wider restrictions on all gambling on the internet. 888 Holdings tumbled 7.5 percent and GVC was the worst performer on the main index.
Earnings drove direction among the top midcap movers.
After profit warnings, sub-prime lender Provident Financial plunged 20 percent, on track for its worst day since August 2017, and Spire Healthcare dropped 12.3 percent.
Online fashion retailer Boohoo shed nearly 6 percent despite raising its full-year sales forecast after a strong Christmas period.
But Spirent Communications surged 10 percent after forecasting better-than-expected full-year profits.
Flybe sank 40 percent on the small-cap index. Britain's biggest domestic airline agreed to sell some assets and got a revised bridge loan in relation to a takeover offer by a consortium.