Chairman Richard Lapthorne hinted in November that private equity firms - thought to include Permira and Carlyle - had expressed an interest in buying the group, which owns broadband supplier Bulldog.
It is understood that at least one private equity group made an informal approach last summer but was rebuffed by the board.
However, following last week's profit warning and unexpected restructuring, which saw the departure of chief executive Francesco Caio, the interest of potential bidders has cooled. That is even though the restructuring, dividing the company into a UK division and one holding its overseas telecoms arms, would make a break-up bid much easier.
Takeover interest had centred on C&W's struggling UK business. As well as Bulldog, this includes Energis, which the group bought last year, and a retail arm, which provides voice and data services to companies such as Tesco.
Mr Caio is not being replaced, with John Pluthero, the former head of Energis, heading the UK operation.
Last week, the company warned that earnings for the next financial year in the UK would be no higher than in the current year, even though more than half of the savings from the integration of Energis would fall next year. C&W blamed falling margins.
Private equity sources said that a bid is not viable because the UK business is generating so little cash. This would make it difficult for the new owner to pay down the debt needed in a leveraged buyout.
City analysts added that management's high valuation of the company made a takeover unlikely. Its shares closed 15 per cent down at the end of last week. Its UK retail business is suffering from cut-throat competition because there are too many suppliers with expensive networks to fill, and not enough demand.
The integration of Energis is also not complete and management has yet to prove that it can make the estimated savings of £150m.