A total of 29,173 cases were reported by the Government on Sunday (Jul 25), down from the 48,161 recorded a week ago on July 18.
It is the fifth day in a row that the number of daily reported cases has dropped, with average daily cases down 15% week on week.
The last time cases fell for five consecutive days was between February 5 and 9.
However, it is too soon for the data to show any impact from the ending of legal restrictions in England last Monday (July 19) due to the time lag between people becoming infected and getting tested.
Some restrictions remain in Scotland, Wales and Northern Ireland, including limits on indoor gatherings and wearing face coverings in certain areas.
Government figures also show that a further 28 people had died within 28 days of testing positive for Covid-19 as of Sunday, bringing the UK total to 129,158.
Separate figures published by the Office for National Statistics show there have been 154,000 deaths registered in the UK where Covid-19 was mentioned on the death certificate.
Government data also shows that, up to July 24, some 46,563,452 first doses of coronavirus vaccine had been administered in the UK, with 37,160,659 second doses.
Meanwhile, the latest case rates for every local authority in England show that infection levels were rising in the majority of areas last week.
The figures, for the seven days to July 21, are based on the number of people who have tested positive for Covid-19 in either a lab-reported or rapid lateral flow test, by specimen date.
The rate is expressed as the number of new cases per 100,000 people.
Data for the most recent four days (July 22-25) has been excluded as it is incomplete and does not reflect the true number of cases.
Of the 315 local areas in England, 270 (86 per cent) have seen a week-on-week rise in rates, 43 (14 per cent) have seen a fall, and two remain unchanged.
Redcar & Cleveland continues to have the highest rate, with 1,785 new cases in the seven days to July 21, the equivalent of 1,301.5 per 100,000 people.
This is up from 1,268,7 in the seven days to July 14.
Middlesbrough has the second highest rate, up from 1,178.2 to 1,194.5, with 1,684 new cases.
Stockton-on-Tees has the third highest rate, up from 944.5 to 1,081.3, with 2,134 new cases.
The five areas with the biggest week-on-week rises are