The cases are down 35 on yesterday's figure of 7,143, the most since the pandemic began.
Wednesday's deaths are the same as yesterday and take the overall number to 42,143.
The vast majority of new cases and deaths are still in England - 5,656 and 62; with Northern Ireland recording 424 and 1, and Wales 388 and 1.
Seven of the deaths were in Scotland - the highest there since 17 June - and it recorded 640 new cases, down from 806 the day before.
On a weekly comparison, UK cases are 15% higher than the 6,178 recorded last Wednesday, but deaths have nearly doubled from 37.
The deaths figure records people who died within 28 days of their first positive test.
However, COVID-19 may not necessarily be the actual cause of death in all cases.
UK infections are still much lower than the peak of the pandemic when some experts, including chief scientific adviser Sir Patrick Vallance, suggest there were around 100,000 new daily cases.
Only a fraction of the true number of cases are believed to have been picked up as testing was not being done in the community, as it is now.
The current expanded testing regime is of course likely to pick up significantly more cases.
However, the proportion of all tests coming back positive - an important measure - has also increased to above 3% for the first time since 22 May.
Prime Minister Boris Johnson today warned the "only way" to avoid a new national lockdown was to follow the latest coronavirus rules.
Speaking alongside him, England's chief medical officer, Professor Chris Whitty, said there had been a significant uptick in the number of COVID-19 patients in intensive care.
"The direction of travel for both hospitals and intensive care is going in the wrong direction, particularly in the areas that have seen rapid increases in cases," Professor Whitty said.
It comes as tougher restrictions in much of northeast England now make it illegal for people from different households to meet indoors - including in pubs and restaurants.
MPs have also voted overwhelmingly to extend the emergency powers that allow the government to impose such rules.
However, the government will now "wherever possible" offer MPs a vote on new restrictions before they come into force.