Prime Minister Boris Johnson has indicated there will be some “opening up” of foreign travel on 17 May – but said it was important to be cautious.
More details are expected this week to confirm when and how international travel will restart in England.
Speaking on Monday, the PM said “we’ll be saying more as soon as we can” but “we have got to be very, very tough”.
He also said there was a “good chance” of the one-metre plus social distancing rule being scrapped on 21 June.
He stressed any decision on changing the rules was dependent on the data.
On Monday, Public Health England reported 1,649 new cases alongside a single death within 28 days of a positive test across the UK.
The recorded number of daily deaths is often lower at weekends and on bank holidays due to delays in reporting.
Fifty million doses of coronavirus vaccine had now been administered across the UK, Health Secretary Matt Hancock confirmed.
Mr Johnson was speaking after a group of MPs called on the government to keep travel rules in place beyond mid-May.
Foreign holidays are currently banned, but a traffic light system of rules is going to be introduced with countries classed as green, amber or red.
Travellers to green countries will not need to isolate on their return, but they will need to take a Covid test.
Arrivals from amber countries will need to quarantine, while red-list countries have the strictest rules, with only UK or Irish nationals allowed to return and they must pay to stay in a government quarantine hotel.
Further details are expected this week, after the government said it will “set out by early May” how countries will be categorised.