Tube maintenance firm Metronet has sent London Underground (LU) a bill for almost £1bn for extra improvement work on the network.
Metronet is responsible for improving two-thirds of the Tube
Metronet is investing £17bn over the next 30 years under a public-private partnership (PPP) scheme.
But it estimates there will be a £1.2bn overspend after seven-and-a-half years.
The private consortium claims LU should foot the bill, but LU said the overspend was due to Metronet's inefficiencies and so it should pay.
But the firm says some of the blame lies with LU for forcing it to do work it was not originally contracted to do under the PPP contract.
Metronet chairman Graham Pimlott said failure to reach an acceptable solution had left them with no option.
"Where we have made mistakes our shareholders have borne the costs.
"However the PPP terms are clear - where additional spending is required to meet London Underground's demands then we are entitled to be paid," he said.
In February, London Mayor Ken Livingstone called for an independent review into Metronet's economic performance.
It followed a report by the PPP arbiter which found the company, which is responsible for the maintenance and renewal of two-thirds of the underground network, would overspend by £750m.
An LU spokesman said: "Metronet has not provided evidence to date that any additional payments would have been required by a competent organisation.
"It therefore remains of the belief that Metronet's projected cost overrun should be largely or entirely borne by it and its shareholders."
Metronet is now taking its case to the PPP arbiter, who will review the matter and make a judgement in nine months.