Doctors say many units are already over-stretched and struggling to treat all their patients.
Hospitals are having to treat patients at night because they cannot fit everyone in during the day.
St George's Hospital in Tooting, south London, is typical of the current shortage.
High costs
Doctors there say they are treating twice as many dialysis patients as the unit is equipped for.
Dr Chris Streather, from the hospital, said it is a picture which is repeated across the capital.
Dr Streather said: "At the moment we are desperately short of dialysis facilities locally and if you were to ask any physician working in any London hospital they would tell you the same thing."
The number of kidney patients is growing by 10% every year as more people develop conditions such as diabetes and high blood pressure.
It currently costs £24,000-a-year to treat a patient who needs dialysis.
Consultants are warning that unless the funding is made available to pay for more dialysis machines London will soon face a crisis.
'Terrible worry'
But the British Kidney Patient Association (BKPA) placed the blame for the current situation on NHS trusts squandering money.
Elizabeth Ward, founder president of the charity, said: "I think the situation in the capital is abysmal.
"Thousands of patients are not sure if they will be getting life-saving treatment and it is a terrible worry for both the patient and the doctor.
"The problem lies with the people who operate the NHS trusts, who quite frankly can't run a fish and chip shop.
"Of course they could do with more money from central government but what they do get they waste."
The association currently funds six social workers throughout the country to help dialysis patients and builds satellite dialysis clinics to supplement the service offered by the NHS.