But the United States, where the pandemic has already claimed 68,700 lives, warned of a further surge in fatalities and Russia became the new hotspot of infections in Europe.
Deaths in Britain are now over 32,000, according to the latest figures from the Office for National Statistics - the highest single-country toll in Europe.
"No country reports on death registrations data as fast, frequently, or to such breadth and depth as we can in the UK," Nick Stripe, head of health analysis at the ONS, said on Twitter.
Elsewhere in Europe, hard-hit Italy, Spain and France have reported a levelling off of figures, offering hope life could start returning to normal.
Many governments in the west were stepping up the pace in easing stay-at-home measures in a bid to revive badly hammered economies, with experts warning of a global recession not seen in decades.
Financial markets saw a light at the end of a tunnel as businesses in Europe and the United States tentatively reopened, and stocks and oil prices rallied Tuesday.
Governments are walking a tightrope between breathing life into stalled economies while preventing a new wave of deadly infections.
Underscoring warnings from experts, an internal government estimate in Washington forecast that the COVID-19 infection rate in the US could surge eightfold to 200,000 a day by June 1, and the daily death toll could rise to 3,000.
Russia meanwhile reported the highest number of new infections among any European country, raising its total to more than 155,000 cases.
"The threat is apparently on the rise," Moscow mayor Sergei Sobyanin has warned, urging residents to respect confinement rules in the capital.
Wearing masks on Moscow's metro system could soon become compulsory, a representative told AFP, and face coverings and gloves were already being sold in vending machines in stations.
The lockdown has however had an unintended side-effect - reported cases of domestic violence in Russia have more than doubled.
Meanwhile, a war of words between the US and China heated up - fuelled by American claims the virus originated in a Chinese laboratory, a theory the World Health Organization (WHO) labelled "speculative".
Since the disease first surfaced in China late last year the number of confirmed cases has reached almost 3.6 million and fatalities have topped 251,000.
But the claim from US President Donald Trump was rejected on Monday both by the WHO and top US epidemiologist and government adviser Anthony Fauci.
"Everything about the stepwise evolution over time strongly indicates that (this virus) evolved in nature and then jumped species," he said.
Trump has acknowledged that deaths will go beyond his earlier prediction of 60,000, saying: "We're going to lose anywhere from 75, 80 to 100,000 people."
Economic casualties were also piling up from the impact of the pandemic.
Spain added 280,000 people to its jobless ranks, while Virgin Atlantic airlines said it would have to fire one in three staff as the virus grounds planes worldwide.
On Monday US manufacturing giant General Electric announced it will cut an additional 10,000 jobs from its aviation sector as the pandemic decimates the industry.
The economic fallout prompted the US Treasury to announce it will borrow a record $3 trillion in the April-June period, largely to finance spending on virus relief programmes.
In Australia officials said the economy is losing Aus$4 billion (US$2.5 billion) every week the shutdown continues, with GDP forecast to plunge 10 percent in the June quarter.
Across Europe, millions of people eased into post-lockdown life this week - revelling in being allowed out despite anxiety over the economic havoc wreaked by the pandemic and a much-dreaded second wave of infections.
"We are all afraid," said Cristina Jimenez in Spain. "Who hasn't lost their job already may lose it in the next few months," she said.
"But what is important is that we are well. With work, you can always find another."
Germany, which has been a step ahead of large European neighbours on lifting curbs, will see restaurants reopen in some regions as early as mid-May.
And as France prepares to lift its shutdown next week, the Paris mayor announced that some busy roads will be reserved for bicycles to try to limit the crowds on public transport. In India, police had to wade in to separate people jostling to buy alcohol for the first time in 40 days as the world's biggest lockdown eased.