Thousands of households could see council tax rise by as much as 32% next year.
Three London boroughs - Barnet, Bromley and Lambeth - have each applied to the Government for authority to exceed the usual 5% cap on council tax in order to plug sizable budget gaps.
The move follows earlier warnings from two other London councils that they may need to lift bills by 150% and 94% respectively.
Council tax is normally adjusted each April and limited to a 5% increase, but local authorities may seek special permission for higher hikes.
Financial strain on councils in London and the South East has grown since Labour introduced the Fair Funding formula last year, which directs more money to deprived areas while leaving wealthier councils with significant shortfalls.
These authorities now intend to raise tax rates to offset the drop in central funding.
Residents could find it harder to meet the higher bills, with some possibly forced to relocate.
Barnet is negotiating a 32% increase that would lift the average Band D bill from £1,622 to £2,060 annually.
The Labour-run borough says it faces a £200 million shortfall by 2030, driven by reduced government grants and rising social care costs, and has already taken emergency loans to avoid bankruptcy.
Conservative-led Bromley has not disclosed a specific rise but is seeking permission to go beyond the 5% limit, saying the Government left it with "no other viable option" after a funding cut of over £30 million.
Lambeth, governed by a Green-led coalition, also wants to exceed the cap; while no final figure is set, the council is dealing with a £130 million funding gap.
Estate agent Hamptons estimates the tax hike would affect nearly 3,600 homes in Barnet, 1,300 in Bromley and almost 3,000 in Lambeth.
Hammersmith and Fulham Council has already warned its residents of a 100%-150% increase, adding £29 a week or £1,508 a year to the average Band D bill.
Wandsworth Council is planning a 94% rise, which could add £958 to the average Band D bill.
Kensington and Chelsea, Westminster and the City of London are also proposing double-digit increases, while Windsor and Maidenhead in the commuter belt is looking at a 25% rise.
The Ministry of Housing, Communities and Local Government told The Times: "We're fixing an outdated system so that funding goes where need is greatest, while protecting councils through the transition and ensuring no area faces a cliff edge."
It added, "For London councils, we're making £11.5bn available - that's more than a 38% increase since 2024-25 - in recognition of the particular pressures facing the capital, such as the high costs of temporary accommodation."
