Internal candidates
Pierre Danon, retail chief
Paul Reynolds, wholesale chief
Likely candidates have been queuing up to rule themselves out of the race for one of the toughest and most high profile jobs in British business.
BT's highly-regarded finance director Philip Hampton, once regarded as the natural successor to Sir Peter, quit the company on Thursday after reportedly clashing with Sir Christopher.
Internal candidates
Another early favourite for the top job, Pierre Danon, the former boss of Xerox Europe who was drafted in as the first head of BT's retail division, has repeatedly made it clear that he is not interested in the top job.
This has not stopped the Frenchman from being appointed to BT's board and he is still seen as the most likely internal candidate.
Head of BT wholesale Paul Reynolds is now seen as only having an outside chance, given his involvement with BT's ill-starred attempt to make its lines available to other operators.
Bookies' favourite
Mike Grabiner, former chief executive of business telecoms group Energis, was, at one stage, the bookies' favourite to land the BT job.
His sudden departure in May from Energis, arguably the UK's most successful fixed line telecom operator over the past five years, without a job to go to has led to frenzied speculation about his next move.
But Mr Grabiner has reportedly told friends he does not want another job in telecoms.
Another fancied runner, Graham Howe, deputy chief executive of Orange, is thought to have been lined up for the top job at the Anglo-French mobile operator, making a move to BT unlikely.
Tony Ball, executive director of satellite broadcaster BSkyB, who has also been linked with the vacant chief executive post at Channel 4, is also reported to have ruled himself out.
Vodafone's boardroom is still a potential hunting ground, but the multi-million pound salaries commanded by chief operating officer Julian Horn-Smith and Northern Europe boss Peter Bamford are likely to put them beyond the reach of cash-strapped BT.
Remaining candidates
Of the remaining possible candidates, Cable & Wireless chief executive Graham Wallace , has previously said he would not like to move but has not so far commented specifically on the BT job.
Mr Wallace is well-regarded within the telecom industry, although his reputation has come under pressure in recent months after a severe Cable & Wireless profit warning.
Gerry Murphy , the straight-talking chief executive of Carlton Communications, has also remained silent on the subject of the BT job.
The Irishman would bring skills in developing programmes that could prove vital to BT's broadcasting ambitions.
He has already proved adept at jumping industries, after joining Carlton from warehouse and distribution giant Exel, but he is regarded as something of an outsider.
Latest contenders
BT insiders say the name being mentioned most frequently in connection with the top job is Rupert Gavin, the head of the BBC's commercial arm BBC Worldwide.
Mr Gavin, a former BT executive who rose to be head of its information and entertainment programme, is credited with turning the BBC's programme sales arm into financial success.
Another contender to have emerged in recent days is Lucy Woods, head of US telecom giant WorldCom's European operations.
She is a former assistant to former BT chairman Sir Iain Vallance, and worked at the company for 15 years.