At least 3.1 million people in England contracted the virus in the week to July 13 - up from 2.9 million the previous week. That means an estimated one in 17 people in England had the virus last week - compared to one in 19 the previous week.
In Scotland, 340,900 people - or one in 15 - had the virus in the week to July 14.
Infections declined from 183,500 to 183,200 the following week in Wales.
In Northern Ireland, infections also dropped to an estimated 88,400 people from 107,600.
The ONS describes the trend in both Wales and Northern Ireland as uncertain.
The percentage of people testing positive for the virus increased to 6.2 per cent in London.
The positivity rate was highest in the North West (6.52 per cent) and lowest in Yorkshire and The Humber (4.5 per cent).
3.8million infections is the highest total recorded since mid-April.
Rates were highest in people aged 16 to 24 and 50-69, and lowest in children aged 6 to 11.
Immunologist Professor Denis Kinane said he is growing “worried that case numbers” are continuing to rise when “we should be expecting a fall”.
He added: “At the same time last summer, the level of infection was far lower at just 1 in 75 people. A surge in Covid infection levels in the Autumn, along with a predicted rise in flu cases, could be a double whammy for our hospitals. We must do all we can to stop the spread of COVID in coming weeks to stop that happening.
“Despite our success in mitigating the impact of Covid through the vaccine programme, we cannot afford to be complacent as hospitals are still under pressure. This virus is still a dangerous and highly infectious disease and it is concerning that the figures continue to rise at a time when we would expect them to fall.
“...The ending of universal free testing along with a largescale reduction in border control measures has meant that the UK’s virus surveillance capabilities have been sharply reduced.
“Speedily recovering international travel and the waiving of the requirements to take pre-arrival and on-arrival Lateral Flow or PCR tests has opened up the UK to additional risks.”
It comes after the World Health Organisation issued a stark warning as Covid cases continue to surge.
European regional director Hans Kluge said the number of cases had tripled in the past six weeks – with almost three million infections last week alone.
It is feared the figures will rise further throughout the autumn and winter as schools reopen, people return from holidays and social mixing moves indoors.
Mr Kluge said countries should increase vaccine uptake and offer second boosters to at-risk groups as well as promoting masks.
He added: "Waiting for the autumn to act will be too late.
"If health authorities act now then they can help reduce the anticipated disruptions to society, including health worker absences and overburdened health systems, struggling businesses and travel chaos."