The new interim data, published on Friday, also shows that around one in 35 people in private households in England had Covid-19 in the week to December 19 - up from one in 45 in the seven days to December 16.
This is the highest estimate for England since the ONS began estimating community infection levels for England in May 2020, and is equivalent to around 1.5 million people.
In London this rises to around one in 20 people likely to test positive for Covid-19, the highest proportion for any region in England, the ONS said.
North-east England had the lowest proportion, at around one in 55.
ONS chief Sir Ian Diamond said there were "some indications" of people engaging in "safer behaviour" in response to the Omicron wave, but, he told BBC Radio 4's World At One programme: "At the moment I think it's far too early to suggest that we will see anything other than a continued rise."
Sir Ian said the "sobering" figures showed "really big increases" in Covid-19 cases, with London "clearly the epicentre of the Omicron epidemic" with numbers going up "really steeply".
He added: "There are increases right across England, with the slight exception of the South West, increases in Wales and Northern Ireland, and Scotland has gone up just a little bit."
The ONS also said that Covid infections compatible with the Omicron variant have increased in all regions in England with "substantial regional variation", with the highest rates in London and the lowest in the North East.
In Northern Ireland, the latest estimate is one in 40, equalling the record from mid-August, while for Scotland the latest estimate is one in 65, below September's peak of one in 45.
The Government confirmed that a further 122,186 lab-confirmed Covid-19 cases had been recorded in the UK as of 9am today (Christmas Eve), another new record for daily reported cases.
Meanwhile, the UK Health Security Agency (UKHSA) said there had been 23,719 additional confirmed cases of the Omicron variant reported across the UK, bringing the total to 114,625.
The number of deaths in England of people with the Omicron variant has risen to 29, and hospital admissions in England for people with confirmed or suspected Omicron rose to 366.
The latest figures come after UKHSA chief executive, Dr Jenny Harries, said data suggesting Omicron may be less likely to lead to serious illness than the Delta variant of coronavirus offers a "glimmer of Christmas hope".
But she warned that it is too early to downgrade the threat from the new strain, which is still spreading rapidly across the UK.
Dr Harries said: "What we have got now is a really fine balance between something that looks like a lower risk of hospitalisation - which is great news - but equally a highly transmissible variant and one that we know evades some of our immune defences, so it is a very balanced position."