Sterling was close to its 200-day moving average of $1.27 against the dollar on Monday, last trading down 0.1% at $1.2603.
Against the euro, the pound fell 0.5% to 89.98 pence , not far its 55-day moving average at 89.30 but failing to break 90 pence.
Boosted by improved risk sentiment and hefty fiscal stimulus recently announced by finance minister Rishi Sunak, the British pound is attracting investor attention, rising nearly 2% so far this month.
Second only to the Norwegian crown, sterling has been the best-performing currency in July as traders moved into riskier assets such as equities, buoyed by hopes of an economic recovery post-COVID-19.
On Monday, European shares were in positive territory as markets looked to earnings season, expecting most U.S. companies to beat forecasts as the bar has been set low.
"The pound remains strongly positively correlated with the performance of global equities," said Lee Hardman, currency analyst at MUFG.
"According to our calculation, the 30-day rolling correlation between daily percentage changes in GBP/USD and MSCI ACWI index remains elevated at +0.56," Hardman said.
Britain's imminent exit from the European Union, however, still weighs on investors' minds.
Britain is urging businesses and individuals to prepare for the Dec. 31 end of the Brexit transition period with an information campaign titled: "The UK's new start: let's get going."
But a survey from lobby group the Institute of Directors said only a quarter of companies were fully ready for the end of the transition period.
Britain left the EU on Jan. 31, three and a half years after a referendum, but a transition period has delayed any major change in the relationship.
Jane Foley, senior currency analyst at Rabobank, said the fact that euro/sterling has been unable to push convincingly below the 89.5 level suggested that "sterling's good run may have run out of steam."
She said she recommends "buying EUR/GBP on dips with the view that another move back above the 90 level is likely," citing reasons such as Brexit uncertainty, the shock of the COVID-19 lockdowns, and the lingering talk of interest rates going into negative territory.
Rabobank sees euro/sterling rising to 92 pence in three months, Foley said.
(Reporting by Olga Cotaga, editing by Larry King) ((email@example.com))