Donald Trump's visit to the UK in the next week will put "unquestionable pressure" on UK police forces, the Police Federation has warned.
The US president will spend time in London, Windsor and Scotland during the two-day working visit.
Thousands are expected to protest and police forces from across the country have been asked to send officers to assist.
The Home Office said other forces can be "recompensed by the hosting force".
Forces assist one another outside their regions when dealing with major incidents and emergencies, under the so-called "mutual aid" agreement.
Mr Trump's visit will see thousands of officers deployed from their home forces, said Simon Kempton, from the Police Federation of England and Wales.
"The fact cannot be ignored that while the officers on mutual aid are deployed elsewhere thousands more of their colleagues left behind in their home force will be expected to pick up the slack, leaving them even more stretched," he said.
"There was a time when we could do it all but now choices have to be made - we cannot do it all and this type of event puts a service which is already creaking at its knees under unquestionable pressure."
Mr Trump will fly to the UK on Thursday afternoon with First Lady Melania Trump, following a Nato summit in Brussels.
The couple will attend a black-tie dinner on Thursday at Blenheim Palace in Oxfordshire, before spending the night at Winfield House in London.
On Friday, the president will travel to Chequers in Buckinghamshire for bilateral talks with Theresa May. In the afternoon, he will meet the Queen in Windsor and then fly to Scotland, where the couple plan to spend the weekend.
Thousands are expected to protest in London on Thursday and Friday and marches are also planned for Scotland, where Mr Trump owns golf courses.
The Treasury has confirmed it will fund policing costs of up to £5m in Scotland.
With officers sent in to help, local policing was being reduced to a "reactive service", Mr Kempton said, with additional strain due to the World Cup and the Novichok poisonings in Amesbury.
"You have to ask what would happen if we're unable to resource incidents like these," Mr Kempton added.
"Would we see the situation where the military were drafted in place of police officers? Green uniforms instead of the blue ones people would - and should - expect to see? It's a worrying prospect."
The National Police Chiefs' Council said discussions were ongoing about "how the resource requirements of this massive operation will be met" but a spokesman said: "We are confident that forces will continue to maintain local policing services."