More than 60 NHS staff - mainly GPs, but including practice managers and consultants - signed the letter to express their 'dismay' at the level of funding Tower Hamlets CCG receives.
The group warns that while the population of the area has surged by more than 12% over the past four years, the CCG's funding allocation has risen by less than 9% - effectively leaving the CCG £12.5m short of the funding it received four years ago.
The warning from London GPs follows warnings from GPs across the country that their practices could struggle to cope as winter drives up pressure on the health service.
GPonline reported last week that two thirds of GPs believe their practice will struggle to cope this winter. Meanwhile, 90% said the NHS as a whole would struggle to cope.
Figures published last week by NHS England appeared to confirm that the health service is already struggling with the worst of winter yet to come - 94.5% of acute and general hospital beds in England were occupied in the week to 3 December, well above the 85% target. GPs have warned this will create a knock-on effect for primary care.
The Tower Hamlets GPs say that the current funding formula for general practice fails adequately to recognise the impact of deprivation and the fast turnover among the population that primary care services in London support.
But they warn that although the formula must be updated, overall NHS funding must be increased to avoid 'robbing Peter to pay Paul'.
'We know that we are not alone in struggling to provide the healthcare that our population needs and deserves,' the GPs write. 'We know that all over England the NHS, both primary and secondary care, is teetering on the brink of collapse, often kept going by the goodwill of staff who go the extra mile due to dedication to the job.
'This situation is not necessary. We are the fifth largest economy in the world.'