The policing costs alone for Donald Trump’s trip to the UK could exceed £10 million, security planners have said, making it potentially the most expensive state visit in British history.

The presidential visit is expected to attract even larger, angrier crowds than seen at two major demonstrations since the inauguration — the Women’s March and protests over Mr Trump's travel ban, which between them brought more than 100,000 people to the streets of London.

Controlling protesters would require a police deployment similar to the G20 Summit in 2009, which cost the Metropolitan Police more than £7.5 million, a source told The Times.

A petition to cancel the visit has reached nearly two million signatures, and a parliamentary debate on the subject has been tabled for later this month.

But so far Downing Street has not indicated it is seriously considering revoking the invitation to Mr Trump, saying: “We look forward to hosting the president later this year.”

A YouGov poll for The Times found that despite widespread disapproval of the president and his policies, 49 per cent of voters think the visit should go ahead because Britain has to deal with the elected leader of the US. It found 36 per cent of voters in favour of withdrawing the invitation.

Buckingham Palace has expressed more unease at the prospect of the visit than Downing Street. Prince Charles in particular has clashed with the new President over climate change. He also warned the lessons of the Second World War are in “increasing danger” of being forgotten at a fundraiser for World Jewish Relief, held shortly after Mr Trump's travel and immigration ban on people from seven majority-Muslim countries, including refugees, was implemented.

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Members of the President's staff have warned that Prince Charles should not “lecture” him on climate change during the visit in case the fiery politician “erupts” in return, The Sunday Times reported.

Mr Trump has reportedly expressed a preference that the younger generation of royals, such as Prince Charles’ sons William and Harry, meet him instead. Although this could also be awkward: an old tweet Mr Trump sent about Kate Middleton, Prince William's wife, in 2012 has recently resurfaced. The former reality TV star weighed in on the furore around the publication of topless photos of Kate Middleton, saying the Duchess of Cambridge only had herself to blame for the photos being taken.

The last major state visit, by President Xi of China in 2015, cost the Metropolitan Police £1.1 million. Protests against his presence mainly involved small Free Tibet groups and were easily contained.