The pound rose against both the dollar and the euro overnight before steadying early on Tuesday, recovering somewhat from seven-week lows but not fully participating in a market-wide relief rally from improving risk appetite.
Positive signs from a coronavirus antibody trial saw safe-haven currencies, such as the dollar, fall as markets rallied.
But downside risks continue to weigh on the pound. The market has started to price in the possibility of negative interest rates.
"GBP lagged in the risk recovery yesterday as prospects of a looser monetary policy and the idiosyncratic risk of UK-EU trade negotiations have taken their toll on the currency," ING analysts wrote in a note to clients.
The pound's overnight strengthening was small in relation to its recent downward trajectory.
Versus the euro, the pound had hit a seven-week low against the euro on Monday at 89.60 pence, but it strengthened to as much as 89.19 pence at around 0630 GMT. It was last at 89.28, up around 0.2% since New York's close.
Against the dollar, the pound had slipped below $1.21 on Monday. It hit a low of $1.2185 around 0320 GMT on Tuesday before recovering to as much as $1.2268 in early London trading . It was last at $1.2243.
A Bank of England rate-setter, Silvana Tenreyro, said late on Monday that the central bank has not ruled out negative interest rates.
This added to speculation after the bank's chief economist, Andy Haldane, said in a newspaper interview on Sunday that negative rates were being looked at more urgently.
"The relatively disappointing performance of the pound was driven again by further speculation over the prospect of negative rates in the UK," Lee Hardman, currency analyst at MUFG, wrote in a note to clients. "The heightened uncertainty is set to remain a weight on the pound."
Brexit also continues to deter pound investors, after the latest round of negotiations ended with scant progress on Friday.
The UK announced a new post-Brexit tariff regime on Tuesday morning to replace the European Union's external tariff, maintaining a 10% tariff on cars but cutting levies on tens of billions of dollars of supply chain imports.
With a death toll topping 40,000, the UK has overtaken Italy as the worst hit by coronavirus in Europe.
A measure of UK jobless claims rose to its highest since 1996 in April, the first full month of the government's coronavirus lockdown, data published on Tuesday showed.