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Speaking at the daily government briefing, Health Secretary Matt Hancock said he was 'appalled' by the events in the US, but said people must follow social distancing rules for the safety of their families.
He said: "Like so many I am appalled by the death of George Floyd... but we are still facing a health crisis.
"Please, for the safety of loved ones, do not attend large gatherings including demonstrations of more than six people."
His warning comes as thousands of people across the country have taken to the streets to protest since 46-year-old black man George Floyd died in police custody on 25 May.
Earlier today, it was confirmed that more than 40,000 people have now died in the UK after testing positive for coronavirus.
The death toll increased by 357 from Thursday, taking the total to 40,261. This means the UK has the second highest death toll in the world, behind the US.
Indeed, the UK reported more deaths on Wednesday (359) than all the EU countries combined, which totalled 345 deaths across 27 nations.
What's more, the UK's death toll is believed to be at least 10,000 higher according to numerous statisticians, including the Office for National Statistics, who factor in 'excess deaths'.
These are deaths that may not have occurred in ordinary circumstances, and this figure is calculated by comparing data with the average number of deaths that occurred in the same period in the previous five years.
As of 9am 5 June, there have been 5,214,277 tests, with 207,231 tests on 4 June.
283,311 people have tested positive.
As of 5pm on 4 June, of those tested positive for coronavirus, across all settings, 40,261 have sadly died.
- Department of Health and Social Care (@DHSCgovuk) June 5, 2020
Speaking at prime minister's questions on Wednesday, Boris Johnson defended the Government's response to the pandemic.
He said: "I take full responsibility for everything this government has been doing in tackling coronavirus and I'm very proud of our record.
"If you look at what we have achieved so far, it is very considerable. We have protected the NHS, we have driven down the death rate."
Johnson has also previously claimed direct comparisons with other countries can be misleading, as deaths are recorded differently and of course population sizes differ.
The weekly rate of deaths and infections is also falling and the Government is gradually easing lockdown measures, with gathering in socially distanced groups of six permitted as of Monday.
Speaking back in March, before lockdown measures were introduced, Sir Patrick Vallance said keeping the death toll below 20,000 would be 'a good outcome in terms of where we hope to get to with this outbreak'.