Murray followed CEO Adam Singer out of the cable firm last week, after three years in post. Singer was ousted by the company's board last week amid concerns at Telewest's ongoing financial problems.
The company's share-price has collapsed from a dotcom boom era high of 560p in March 2000, to just 2p this week.
A Telewest spokesperson confirmed that Murray would not be replaced, and that director of PR Jane Hardman would now assume a combined director of corporate communications role.
Hardman now oversees a staff of 10 across corporate comms, industrial relations and public affairs.
She also oversees the work of three agencies: consumer agency Consolidated Communications; issues management consultancy Luther Pendragon; and corporate and financial agency Brunswick.
Former Daily Express executive editor Murray said he expects to provide consultancy advice to Telewest, but played down rumours he would found his own agency: 'The idea is pretty nascent at the moment but it would be a bit strong to call it an agency. I'm not looking to go the full-scale agency route at the moment, I'm looking more at it being just myself as a consultant, although that may expand.'
Murray admitted the departure of Singer - who brought Murray to the position from Flextech when it merged with Telewest - was behind his departure: 'It's no secret that I was very close to Adam Singer, and when he went, I think it was the right time for me to go, too.'