After sliding from a 2018 high of more than $1.43 in April to below $1.33 as a resurgent dollar hit the currency and expectations of a Bank of England interest rate rise collapsed, the pound has since edged slightly higher.
Data this week, including a widely watched survey of the dominant services sector on Tuesday, suggest weaker economic momentum in the first quarter was temporary and the economy is recovering.
Sterling rose 0.2 percent to $1.3426, but fell 0.2 percent against the euro to 87.635 after strong gains versus the single currency on Tuesday.
"While yesterday's data is good news for the pound, it can't be viewed in isolation to the Brexit risks that are becoming a more dominant influence on the outlook for the economy," MUFG analysts said. "We remain sceptical over pound gains on positive macro news until we have clarity from the government on Brexit."
A political crisis in Italy and an escalating trade dispute between the United States and other major economies have meanwhile dominated trading in currency markets in the last week, keeping sterling flows relatively quiet.
Still, major risks are on the horizon for the British currency.
Diplomats are hoping an EU summit on June 28-29 can break a deadlock over the terms of Britain's divorce from the bloc, with time running out before Britain formally leaves in 2019.
But with major sticking points over the Northern Irish land border with the Republic of Ireland and over a future agreement for financial services, some British officials have suggested the outlines of a deal will not be announced until later in the year.
"There's plenty of Brexit news, but irrespective of the news flow we are still in the same position. We are no closer to knowing the relationship Britain is going to have (with the EU)," said Jane Foley, a currencies strategist at Rabobank, adding that many investors were waiting it out in the meantime.
Investors would also need to see more than one month of solid economic data before expecting the BoE to raise rates, Foley said. Money markets are pricing in a 60 percent chance of a 25 basis point rate rise in September.