Mr Cameron stopped short of revealing whether he felt the former DJ should lose the honour, but suggested that the case should be considered by a Whitehall committee which has the power to recommend forfeiture.

His comments came after the chairman of the BBC Trust backed inquiries by police and the corporation.

Lord Patten said the allegations against Savile could not be excused as behaviour from a time when "attitudes were different".

He told a business dinner in Cardiff it was "no excuse to say 'That was then' in the 1960s, '70s and '80s, and attitudes were different then. It's no excuse to say 'I'm sure the same thing used to happen with pop groups and others at the time'. Those things may be true but they don't provide an excuse."

The radio and TV presenter and charity fundraiser, who died in 2011, has been accused by a growing number of women in the last few weeks of sexual abuse.

Mr Cameron said today: "We have something called a Forfeiture Committee. It is responsible for looking at honours and the removal of honours, and obviously they have to do their job too."