Almost all London boroughs recorded more than 1,000 Covid cases per 100,000 people on Monday.
In Wandsworth and Lambeth the infection rate was over 2,000, according to the latest Government data.
Infections are highest in younger adults, particularly those aged 25 to 29, in inner London boroughs.
Lambeth recorded an infection rate of more than 5,000 in the age group in the week ending December 15.
The soaring numbers of people testing positive comes as an estimated four million Londoners prepare to leave the capital to visit relatives across the UK for Christmas this week.
After a lengthy Cabinet meeting on Monday, Boris Johnson did not announce further Covid restrictions to help prevent the spread of the Omicron variant.
However, he said he is following the data and warned rules could be tightened in the days ahead as hospitalisations rise.
"Unfortunately I must say to people that we will have to reserve the possibility of taking further action to protect the public, to protect public health, to protect our NHS," the prime minister said.
"We are looking at all kinds of things to keep Omicron under control and we will rule nothing out.
"But at the moment, what I think we want people to focus on is exercising caution - so ventilation, masks in the appropriate places, all the usual stuff about washing hands, but remember how contagious Omicron really is."
Redbridge, Brent, Barnet, Hillingdon, Hounslow, Harrow were the only boroughs to record an infection rate lower than 1,000 cases per 100,000 people.
However all six areas are on course to hit the milestone before the end of the week.
Mr Johnson added: "We have got cases of Omicron surging across the country now.
"We have got hospital admissions rising quite steeply in London and the obvious conclusion is that it was right to go fast with Plan B in the way that we did and also right to double the speed of the booster rollout.
"In view of the balance of risks and uncertainties, particularly around the infection, hospitalisation rate of Omicron - how many people does Omicron put in hospital - and some other uncertainties to do with the severity, the effectiveness and so on we agreed that we should keep the data from now on under constant review."
Covid infection figures for every London borough:
.Merton - 2845 cases, up 1,594 (127.4%) Case rate per 100,000 people 1,378.0
.Southwark - 5767 cases, up 3,839 (199.1%) Case rate per 100,000 people 1,802.1
.Waltham Forest - 3471 cases, up 1,918 (123.5%) Case rate per 100,000 people 1,253.3
.Havering - 3019 cases, up 1,507 (99.7%) Case rate per 100,000 people 1,158.3
.Islington - 4150 cases, up 2,845 (218.0%) Case rate per 100,000 people 1,672.6
.Sutton - 2399 cases, up 909 (61.0%) Case rate per 100,000 people 1,155.0
.Tower Hamlets - 4865, up 3,331 (217.1%) Case rate per 100,000 people 1,465.5
.Kingston - 2169 cases, up 1,068 (97.0%) Case rate per 100,000 people 1,210.8
.Lambeth - 6774 cases, up 4,730 (231.4%) Case rate per 100,000 people 2,104.9
.Hackney and City of London - 5245 cases, up 3,610 (220.8%) Case rate per 100,000 people 1,797.0
.Westminster - 3184 cases, up 2,042 (178.8%) Case rate per 100,000 people 1,179.9
.Redbridge - 2817 cases, up 1,255 (80.3%) Case rate per 100,000 people 921.6
.Kensington and Chelsea - 1924 cases, 1,159 (151.5%) Case rate per 100,000 people 1,226.5
.Bexley - 2786 cases, up 1,351 (94.1%) Case rate per 100,000 people 1,117.5
.Croydon - 4453 cases, up 2,267 (103.7%) Case rate per 100,000 people 1,146.0
.Richmond - 2462 cases, up 1,073 (77.2%) Case rate per 100,000 people 1,242.5
.Lewisham - 4630 cases, up 2,745 (145.6%) Case rate per 100,000 people 1,516.5
.Brent - 3103 cases, up 1,664 (115.6%) Case rate per 100,000 people 946.7
.Newham - 3634 cases, up 2,065 (131.6%) Case rate per 100,000 people 1,022.9
.Bromley - 4187 cases, up 2,068 (97.6%) Case rate per 100,000 people 1,258.3
.Hammersmith and Fulham - 3128 cases, up 1,915 (157.9%) Case rate per 100,000 people 1,704.2
.Hillingdon - 2382 cases, up 1,029 (76.1%) Case rate per 100,000 people 770.8
.Greenwich - 3908 cases, up 2,087 (114.6%) Case rate per 100,000 people 1,352.1
.Wandsworth - 6676 cases, up 4,583 (219.0%) Case rate per 100,000 people 2,024.7
.Hounslow - 2306 cases, up 928 (67.3%) Case rate per 100,000 people 848.5
.Camden - 3495 cases, up 2,218 (173.7%) Case rate per 100,000 people 1,250.4
.Enfield - 3258 cases, up 1,728 (112.9%) Case rate per 100,000 people 976.7
.Barking and Dagenham - 2291 cases, up 1,173 (104.9%) Case rate per 100,000 people 1,070.0
.Ealing - 3450 cases, up 1,684 (95.4%) Case rate per 100,000 people 1,013.7
.Haringey - 3596 cases, up 2,292 (175.8%) Case rate per 100,000 people 1,350.1
.Harrow - 2086 cases, up 1,004 (92.8%) Case rate per 100,000 people 826.7
.Barnet - 3684 cases, up 1,738 (89.3%) Case rate per 100,000 people 923.3
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