London's weekly rate is 858 cases per 100,000 people, double the UK figure.
And the numbers being admitted to the city's hospitals means the UK-wide total for people in hospital with Covid has already passed the spring peak.
Prof Andrew Goddard, of the Royal College of Physicians, said the virus's new variant was spreading nationwide.
Case numbers were "mild" compared with where he expected them to be next week, he said, and doctors were "really worried".
Half of the major hospital trusts in England are said to be dealing with more Covid-19 patients than at the peak of the first wave in April, with the NHS having its "busiest winter ever".
On Friday, hospital bosses warned the next few weeks would be "nail-bitingly difficult" as cases of the new variant - which is up to 70% more infective - topped 50,000 for the fourth consecutive day.
The most recent UK-wide statistics, from 28 December, showed there were 23,823 people in hospital with Covid. That was already significantly higher than the spring peak, which reached 21,683 on 12 April.
Only English hospitals have released figures for the final three days of December - and these show that a further 2,302 Covid patients were occupying hospital beds on 31 December.
More about: UK coronavirus
