Against a weaker dollar, the pound was last at a six-day high of $1.2265, up 0.6% since New York's close.
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Johnson said at a news conference on Monday that outdoor markets and car showrooms could reopen from June 1 and all other non-essential retail from June 15 if the government's tests are met.
Opening up pubs, restaurants and bars after the coronavirus lockdown is difficult, however, and there will be no standing at the bar in pubs for a long time, Cabinet Office Minister Michael Gove said on Tuesday.
"GBP is enjoying a brief reprieve after a tough couple of weeks, potentially buoyed by the news that the UK retail sector will open up in mid-June," ING strategists wrote in a note to clients.
"However, EUR/GBP will struggle to break below 0.8900, before a familiar impasse on negotiations with Brussels should take its toll as June progresses," they added.
Against a weaker dollar, the pound was last at a six-day high of $1.2265, up 0.6% since New York's close. It has held below $1.23 for nearly two weeks.
Versus the euro, the pound was last at 89.165 pence, up around 0.2%, having strengthened overnight before erasing some gains in early London trading.
The pound is still the worst-performing G10 currency this month, with cable having lost 3% since its peak at the end of April.
According to weekly futures data, short positions on the pound have increased for the past eleven weeks straight . The last time the market was this short on the pound was December 2019.
The pound is weighed down by the UK's high COVID-19 death rate, the fact that the Bank of England is considering negative interest rates, and ongoing Brexit-related risks, as the UK insists it will not seek an extension to the transition period.
The Bank of England's chief economist, Andy Haldane, is due to speak at a webinar organised by the Confederation of British Industry at 0900 GMT.