A review of lockdown measures will take place later this week.
UK ministers have said they want to be sure the country is past the peak of the outbreak before easing the restrictions, but 10 Cabinet members are reportedly calling for the lockdown’s relaxation amid concerns about its impact on the economy.
The Times quoted one unnamed minister as saying it was important not to do “more damage”, and that measures could be eased after another three weeks.
Latest coronavirus news, updates and advice
Scientific advisers will meet on Tuesday ahead of a formal review of the measures on Thursday.
Wuhan, in China, where the outbreak appears to have started, has been back to work for a week after nearly three months in lockdown.
Meanwhile, several European countries, including some of the hardest-hit, are this week slowly easing their restrictions as non-essential workers get back to work.
They provide a glimmer of hope that the continent could soon start returning to some semblance of normality.
Spain will allow some non-essential employees, such as factory and construction personnel, to return to work on Monday as the death rate in the country slowly falls.
Workers returning include builders, metalworkers, cleaners, factory workers and people involved in sanitation and security.
The country has been under a general lockdown since 14 March, and the measures were toughened even further on 30 March when all non-essential business was shut down for two weeks until Easter.
Other businesses including bars, nightclubs, pubs and restaurants are closed and may remain so for weeks.
On Monday, police were pictured handing out masks at metro stations and those returning to work were being advised to maintain social-distancing.
And the country’s cumulative death toll from the coronavirus rose to 17,489 on Monday, up 517 from 16,972 on Sunday, the Health Ministry said. Confirmed cases totalled 169,496, up from 166,019 the previous day.
The worst day for the virus in Spain was 3 April, when there were 950 deaths.
Italy, which has the second highest coronavirus death toll after the US, will let bookstores, stationery shops and children’s clothing shops reopen, and allow forestry-related work to resume, from Tuesday.
The move comes after the country recorded its lowest number of deaths in three weeks on Easter Sunday, with 431 new fatalities.
Strict lockdown conditions that have been in place since 9 March meant only food stores and pharmacies were permitted to stay open, with Italians only allowed to leave their homes for essential needs.
The country's worst day for COVID-19 fatalities was 28 March, with 971 deaths.
The number of people given intensive care treatment and rates of people admitted to hospital have also been going down for nine straight days.
Italy was one of the earliest countries in Europe to be affected by coronavirus and saw a rapid acceleration of cases in March.
The country is in its fifth week of lockdown to control the spread of the virus, and the strict measures are set to remain until at least May 3, said prime minister Giuseppe Conte.
Italy has recorded 19,899 deaths in total, with a total of 156,363 confirmed cases of COVID-19.
Austria has said it will begin to reopen kindergartens and schools.
Chancellor Sebastian Kurz announced last week that shops under 400 square metres (4,300 square feet) will be allowed to open their doors from 14 April, followed by larger ones from 1 May.
It is hoped that all restaurants and hotels will follow from mid-May.
Other public health measures, such as requiring people to wear face masks in supermarkets and pharmacies, will remain in place. The face mask rule has also been extended to other shops and public transport.
Austria’s death toll is 368, while the total confirmed cases is 13,974.
Schools and daycare centres will reopen in Denmark on Wednesday, allowing some parents to return to work.
Denmark was one of the first European countries to impose a strict lockdown on its citizens, and it has been successful in avoiding a spike in coronavirus cases.
Once the schools return, the Danish government will then consider allowing smaller businesses and shops to reopen on a gradual basis.
However, there has been anger and disbelief from a number of parents at the proposal that primary school children should return to class immediately after Easter.
A Facebook group with thousands of subscribers has been set up by concerned parents called "Mit barn er ikke forsøgskanin for Covid-19" – “My child is not a guinea pig for COVID-19”.
The page has attracted more than 37,000 members since prime minister Mette Frederiksen announced the partial lifting of lockdown measures.
Denmark has had 273 people die after contracting the virus, with 6,369 cases.
Meanwhile, senior politicians in Germany have begun debating a potential easing of restrictions ahead of a meeting with leader Angela Merkel on Wednesday.
On Monday, Merkel and premiers of Germany’s 16 states expect to get recommendations from the German National Academy of Sciences.
The chancellor said they will take heavy considerations for a possible loosening in movement and social distancing rules.
Germany's mortality rate of 2.3% – 23 deaths per 1,000 confirmed patients – is conspicuously lower than that in Britain, France, Spain or Italy.
Germany’s death toll is 3,022. The country has recorded 127,854 cases.
What the World Health Organization thinks
The World Health Organization has warned that ending lockdowns early could be dangerous, especially exit strategies are not managed properly.
"Lifting restrictions too quickly could lead to a deadly resurgence," said WHO chief Dr Tedros Adhanom Ghebreyesus at a virtual press conference.
The current number of coronavirus cases confirmed globally currently stands at 1,851,531.