Andrew Marr has accused the Government of setting “a trap” for the BBC by denying it the right to make popular programmes.

The presenter was responding to the questioning by Culture Secretary John Whittingdale of the BBC’s need to broadcast shows such as Strictly Come Dancing and to screen a late evening bulletin at the same time as ITV.

In an interview with the Radio Times, Mr Marr said: “The problem with that is a lot of the things that we do that come into the non-market failure area are very, very popular, and so I know perfectly well the trap that we’re being set, which is the minute we’re doing the non-popular stuff, they go, ‘Oh, far fewer people are listening to you, watching you, therefore we’ll cut your licence fee’. So you can’t win.”

Britain's Culture Secretary John Whittingdale delivers his keynote speech at the annual Conservative Party Conference in Manchester (Reuters)

Speaking in support of the BBC’s licence fee model, Mr Marr said he would be concerned if the broadcaster were to be dependent on revenue that came directly from Government. “I don’t want to be in a position where politicians will appear on my show and are going to be questioned about something they don’t want to be questioned about but can at any point say to me or any manager at the BBC, ‘Do you know what, any more of this and we might have to cut your money a bit’.”

Marr’s former BBC colleague Robert Peston was confirmed by ITV as host of a rival new Sunday political interview programme. In the interview, Marr warned the newcomer to “not think the programme is about you because it never is”. He said he welcomed the challenge. “Bring it on. Competition is good.”