The ONS said these rises were particularly steep in London, the east of England, and the southeast. It added that these regions have the highest percentage of cases associated with the new variant of coronavirus that was first detected in Kent.
London has been confirmed as the leading coronavirus hotspot in the UK, with the capital recording a sharp rise in cases in the week before Christmas.
At a time when thousands of people were fleeing the city before the implementation of tier 4 restrictions, London had the highest percentage of people testing positive for Covid-19 in the country.
In the week up to 18 December, infections were rising across England, Wales and Northern Ireland, according to the latest survey data from the Office for National Statistics (ONS).
An estimated 2.1 per cent of people in private households in the capital tested positive for Covid-19 in the most recent week. This is followed by southeast England (1.4 per cent) and eastern England (1.2 per cent).
Between 12 and 18 December, 645,800 people are estimated to have had Covid-19 – the equivalent of around 1.18 per cent of the population, or one in 85.
It represents a rise from 567,300 people, or one in 95, who were estimated to have Covid-19 in the week up to 12 December.
While much of the south of England has recorded a large rise in cases – driven in part by the new variant – the north of the country has recorded a decrease in infections.
The ONS said that the percentage of people testing positive in the northwest, northeast, east midlands and Yorkshire and the Humber has continued to fall in the most recent week.
When modelling the level of infection among different age groups in England, the ONS said rates have increased in all groups except for those aged 50 to 69, where there are early signs of an increase, and for those aged 70 and over where there are early signs of a decrease.
Rates remain highest among secondary school children.
The ONS also said that two-thirds of recent positive cases in London, eastern England and the southeast could be the new variant of coronavirus.
In London, 68 per cent of positive cases from 14 to 18 December were estimated to be genetically compatible with the new variant, while in eastern and southeast England the estimate is 65 per cent.
For England as a whole, the ONS estimated 49 per cent of new cases were derived from the new variant.
Meanwhile, Wales has reported one of the most dramatic surges in infections, the ONS said.
An estimated 52,200 people in Welsh households had Covid-19 between 12 and 18 December – the equivalent of 1.72 per cent of the population, or around one in 60.
This is up from an estimated 33,400 people, or one in 90, for the previous week.
Infections are similarly continuing to rise in Northern Ireland, though the ONS said that positive cases in Scotland were falling.
The ONS figures are specific to private residents and do not include people staying in hospitals, care homes or other institutional settings.
Separate data released by NHS England on Thursday showed that 521,594 people in the UK received the first dose of the Pfizer vaccine between 8 and 20 December.
More than 70 per cent of these – some 366,715 – were aged over 80.
This is the first time that NHS England has published these figures since Margaret Keenan, a 91-year-old grandmother from Coventry, became the first person outside of a clinical trial to be given the vaccine on 8 December.