A further 57 deaths were recorded, bringing the total to 148,089.
The rise in infections means a total of 12,559,926 Britons have been infected so far during the pandemic.
It is the first time that all four countries in the UK have reported their daily cases at the same time since December 24, with experts warning that much of the data over the festive period remains patchy.
Wednesday’s infection total represents a rise of 66 per cent in a week.
Meanwhile, a total of 10,462 people were in hospital in England with Covid as of 8am on December 29, according to figures from NHS England.
This is up 48 per cent from a week earlier and is the highest number since March 1.
Boris Johnson said people should enjoy the New Year in a “cautious and sensible way” but has declined to impose restrictions to curb the spread of the virus.
Asked about reports of people travelling across the border from Wales and Scotland into England to celebrate, he told reporters: “I think everybody should enjoy New Year but in a cautious and sensible way.
“Take a test, ventilation, think about others – but above all, get a booster.”
Mr Johnson insisted the vaccination campaign had allowed England to maintain its current level of Covid controls despite Wales, Scotland and Northern Ireland opting for tighter measures.
“The Omicron variant continues to cause real problems. You are seeing cases rising in hospitals,” he told reporters.
“But it is obviously milder than the Delta variant and we are able to proceed in the way that we are.”
However, the prime minister has been urged to “get a grip” as a shortage of lateral flow tests threatens to derail New Year’s Eve plans for millions of people.
Ministers have consistently urged Britons to take a test before socialising to curb the spread of the Omicron variant.
But a survey by the Standard found that just three-quarters of pharmacies in the capital currently had lateral flow tests in stock.
Health Secretary Sajid Javid set out the issues in a call with Tory MP Sir Roger Gale, acknowledging there is not a quick fix to a problem caused by global demand.
A UK Health Security Agency spokesperson said almost eight million test kits would be made available to pharmacies by New Year’s Eve.