It marks a second increase in as many days, following the 27,734 cases registered on Wednesday.
A further 85 people had died within 28 days of testing positive for Covid as of Thursday, bringing the UK total to 129,515.
Separate figures published by the Office for National Statistics show there have been 154,000 deaths registered in the UK where Covid was mentioned on the death certificate.
Government data up to July 28 shows that of the 84,515,367 Covid jabs given in the UK, 46,733,115 were first doses, a rise of 43,873 on the previous day.
Some 37,782,252 were second doses, an increase of 171,341.
It comes as a leading scientist claimed the pandemic is almost over for the UK, with the British population very close to herd immunity.
Cases of Covid have been slowly declining over the last week, despite lockdown restrictions being almost completely lifted earlier this month.
Experts were puzzled by the drop and said school closures, the end of the Euros football tournament and the hot weather meaning more people socialise outdoors could be behind the figures.
However virologist Dr David Matthews from the University of Bristol insists it is likely to mean Britain is close to herd immunity.
He told the Telegraph: “In terms of herd immunity – by which we mean the virus has managed to reach everybody and therefore most people will have a level of immune memory – I suspect we’re very close to it.
“Assuming nothing truly spectacularly left field happens, then this pandemic is pretty much over for the UK. I suspect we will not see a major surge this winter, or any serious levels of fatalities.
“The more we close the gap on the last 10 per cent who haven’t had the vaccine, the better we will be. Everyone will eventually meet the virus and it is far better to do so vaccinated.”
According to ONS figures nearly 92 per cent of UK adults have Covid antibodies, either from being infected by the virus or taking the vaccine.