Capita, the present incumbent supplier, deliberately submitted a bid that broke the terms of the restricted tendering process set out by the council.
Westminster is now left with United Utilities subsidiary Vertex as the sole qualifying bidder for the 10-year deal.
The Westminster situation highlights the problems faced as both customers and suppliers get more experienced in negotiating outsourcing contracts, according to Robert Morgan, chief executive of outsourcing advisory consultancy Morgan Chambers.
"The go-live deadline in Westminster is punishing and the terms are commercially harsh," Morgan told CW360.com. "No supplier can afford to accept risk beyond a certain point. Capita reached that point."
Vertex now faces a serious commercial decision, he added. "They will have to decide whether to take the risk and get the business or try to moderate the terms and let Capita back in. Perhaps it is in Westminster City Council's and the rate payers' best interest to moderate this and ensure a competitive process."
Morgan said that the success of the contract might be in doubt without negotiation. "Westminster is the show case for [the government drive to] e-enable all members of society. It must succeed politically. Early moderation will pay hugely in avoiding headline stories later."
Peter Rogers, chief executive of Westminster council, said any outsourcer would have to satisfy the highest level of service provision and employment practice. The authority was determined to get the contract right, he said.
Capita, which reports its results this week, has won significant new contracts including a deal with the Greater London Assembly to build the systems for Mayor Ken Livingstone's £300m road pricing scheme.
It has also been severely criticised for its role in the government's Individual Learning Account scheme, which was closed down after security breaches.