EDS's six-year contract, which is worth more than£6 million, has been bedevilled with problems since it began in February 1997 - notably the failure to pay housing benefits on time.
Kingston upon Thames has been flooded with complaints from benefit recipients. More than 150 were received between March and September last year, prompting the council to warn EDS that it risked losing its contract unless performance improved.
Graham Cadle, the council's contract commissioning officer, said termination of the EDS deal had been 'held in abeyance' pending a further progress report.
An EDS spokeswoman said: 'Improvements have been made and continue to be made. We are on the right track and for some weeks now we've had no backlog at all.'
The firm has agreed to pay a yet to be decided sum into a trust fund to aid local charitable organisations, including the Citizens Advice Bureau, which have supported those kept waiting for benefits payments.
The spokeswoman said the trust fund scheme had been suggested by EDS after it had been advised that it was not legally able to make direct compensation payments to individual clients.
The contractor has also promised to meet the bill for any compensation payments awarded by the ombudsman. But Kingston upon Thames Labour member Steve Mama, who has been advising victims of the payment delays, said using the ombudsman was a 'long and cumbersome way to obtain relief from the long delays caused by the contractors'.
Mr Mama called for the contract to be brought back in-house.
EDS has being going through a rocky patch with its council contracts in recent months.
Last year, Wandsworth LBC took back benefits work from EDS after complaining about the contractor's 'below-par performance' (LGC, 14 September 1998).