The pound's overnight strengthening was small compared with its recent downward trajectory. It is the worst performing G10 currency so far this month.
"Apart from all the corona problems, concerns about Brexit have arisen again," said Thu Lan Nguyen, FX strategist at Commerzbank.
Britain set out plans for a post-Brexit tariff system on Tuesday.
The pound had hit a seven-week low against the euro on Monday at 89.60 pence, but strengthened to as much as 89.19 pence at around 0630 GMT. It weakened during the day before starting to strengthen around 1220 GMT and was last at 89.325, 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 $1.2247. Sterling-dollar implied volatility gauges with a one-month maturity edged down slightly on Tuesday, still holding near three-week highs.