The television veteran ran out ahead of Harry Potter creator JK Rowling and actor Emma Watson, according to research by pollsters YouGov and campaigners 38 Degrees.
Documentary maker Louis Theroux, inventor Sir James Dyson, actor Sir Ian McKellen, presenter Jeremy Clarkson, comedian Rowan Atkinson, journalist Piers Morgan and outspoken columnist Katie Hopkins also made up the top 10 public figures that British people would like to see as premier.
The Duke of Cambridge and Prince Harry were among the famous faces lined up for a role on the front benches, alongside the likes of writer Stephen Fry and presenter David Dimbleby.
The survey of 1,851 British adults found 37 per cent of respondents aged 25 and over preferred Sir David, while Ms Watson was favourite among 39 per cent of 18 to 24-year-olds.
The research highlighted that the British people value honesty (67 per cent) as the most desirable attribute among politicians and when thinking about their dream Prime Minister respondents cited ‘answering questions directly’ (24 per cent) and trust (15 per cent) as important traits when considering their selection.
Laura Townshend, 38 Degrees director, said: “This is a light-hearted look at which public figures Britain would most like in a fantasy front bench - but it proves that trust, honesty and answering questions directly play a big part in the public’s decision making when it comes to who they would like to lead the country.”