That raises the chances of Britain leaving the EU without a deal, posing risks to its economy, but the blue chip FTSE 100 rose 0.5 percent, inching closer to levels last seen in October, as many of its components derive much of their revenues from outside the UK.
The more domestically focussed FTSE 250 gave up gains and was virtually flat as weakness in the local currency weighed.
The FTSE 250 had opened higher, in a rare break from moving in tandem with sterling and another sign that Brexit uncertainty is upending conventional trading strategies.
The midcap index is usually heavily correlated with the domestic currency as about half of revenue generated by companies on the index comes from the UK.
Spreadex analyst Connor Campbell said both sterling and the midcaps seemed to be holding off until after a five-hour cabinet meeting scheduled for Tuesday.
"On one hand, the lack of majority for any one option is shocking and a major blow as we are running out of time, on the other hand you could see it as nothing has changed," he said.
The pound's dip on Tuesday lifted the more internationally exposed components on the FTSE 100, which earn a big chunk of their revenues in US dollars. British American Tobacco , HSBC, spirits company Diageo and Unilever all rose.
"Overall the atmosphere across equity markets is positive, mainly on those hopes that global manufacturing is turning a corner," said Chris Beauchamp, an analyst at Raymond James.
That helped packaging firm Smurfit Kappa gain 2.4 percent, topping the FTSE 100 leaderboard.
Swimming against the tide was Rolls-Royce with a near 2 percent drop on news that Singapore Airlines had grounded two Boeing 787-10 jets fitted with Rolls-Royce Trent 1000 TEN engines after checks found premature blade deterioration.
Sainsbury's was in the red as well after industry data showed that it lost its status as Britain's No. 2 supermarket group by market share to takeover target Asda for the first time in four years.
Notable among stocks gaining ground was low-cost airline Wizz Air, which jumped 4 percent - its biggest daily rise in three months - after saying annual profit would be in the upper half of a range that it previously forecast on "robust" demand.
Wizz Air's update came in stark contrast to larger rival easyJet, which warned on Monday of weakening demand and softer ticket pricing and sent shares of its peers down in the last session.