After Monday's voting outcomes, the European Union's chief negotiator Michel Barnier warned it is "day after day more likely" that Britain will crash out of the bloc next week without an orderly withdrawal agreement.
Nearing midday in London, the pound was down about 0.3 percent versus both the dollar and euro.
"European markets are mixed... but a weaker pound has helped the FTSE 100 to rise above the gloom," noted Chris Beauchamp, chief market analyst at IG trading group.
The benchmark London FTSE 100 index features several multinationals who earn vast sums in dollars.
"As ever, the pound is the clearest gauge of the market's view on continued (Brexit) uncertainty and is halfheartedly losing ground against the euro and the dollar," said Fiona Cincotta, senior market analyst at City Index.
"Parliamentary disarray is also hitting the euro because a disorderly Brexit has the potential to affect European companies trading with the UK.
"Of the European gauges, the (Frankfurt) DAX is possibly in the worst position to withstand a disorderly Brexit as Germany is already flirting with a recession and if its exports of cars and car parts to the UK are affected it would add to problems already created by the slowdown of trade with China," Cincotta added in a client note.
In another downbeat note for the economic outlook, the World Trade Organization forecast Tuesday that global trade growth would be lower in 2019 than last year.
In its main annual forecast, the WTO revised its prediction for this year down from 3.7 percent to 2.6 percent, citing widespread "tensions" and economic uncertainty, including Brexit and tariffs between the US and China.
- US-China trade talks -
World stock markets mostly rose Tuesday but gains were tempered by profit-taking after a recent rally, though investors remain optimistic over China-US trade talks and the prospect of no hike to American borrowing costs.
A forecast-beating factory report out of Beijing -- which spurred buying across the region Monday -- was followed by a similarly positive US reading, tempering worries about the outlook for the world's biggest and most crucial economies.
Traders are now awaiting the start of the next round of top-level trade talks in Washington, with China and the US noting progress in a meeting last week in Beijing.
A series of olive branch measures from the Chinese side has lifted hopes the two will eventually reach a deal to end their tariffs row, which dragged on equities at the end of 2018.
This week also sees the release of US March jobs data, which are closely watched for an idea about the state of the economy, with the Federal Reserve also using the figures to map its path for monetary policy.
The Fed's recent dovish lean has helped propel a rally across stock markets this year, with other central banks also looking to ease up on their tightening moves.
"Having the central banks take a step back, with the Fed saying that they're going to pause and that they're going to be patient at least toward the end of this year, I think that gives the market a little bit of time" to wait for economic data to turn around, said Victoria Fernandez, chief market strategist at Crossmark Global Investments in Houston.
"Is this a bottom, is this a trend that we're starting to see -- an upward trend? If so that's gonna be positive for all of the markets," she added.
The semi-confident air helped oil prices to extend Monday's strong gains, with support coming from news that OPEC had lowered output even as major producer Venezuela's political and economic crisis deepens.