Police cuts could "reduce very significantly" the UK's ability to respond to a Paris-style attack, Home Secretary Theresa May has been warned.
In a leaked letter, one of the UK's most senior police officers said that mainstream policing was essential in the fight against terrorism.
The cuts are expected to be announced in next week's Spending Review.
The prime minister's spokeswoman said the government would do "everything necessary to keep people safe".
She said the government had protected the counter-terror policing budget since 2010 and had announced further measures to counter terrorism, including extra resources for the security and intelligence agencies.
In other developments:
- EU interior ministers are discussing tightening the external areas of the passport-free Schengen area during an emergency meeting in Brussels.
- Mrs May, arriving at the meeting, said there was a "clear link" between the security of the EU's external borders and security within the bloc. She has also called for urgent action on illegal arms trafficking in Europe.
- NSPCC's ChildLine reported more than 100 calls from children fearing they could be victims of terrorist attacks following last week's events.
It is expected that Chancellor George Osborne could announce cuts to the police budget of more than 20% when he addresses Parliament on Wednesday.
That is more than double what the document suggests is viable to keep numbers at the level required in the event of an attack.
Labour has warned that savings above 10% would be "dangerous".
Shadow chancellor John McDonnell said he had asked George Osborne to take police cuts out of the Spending Review, while shadow home secretary Andy Burnham has written to Mrs May.
The Home Office said it would not comment on a leaked document.
Analysis by BBC political editor Laura Kuenssberg
It's not entirely surprising that days before a big statement from the Treasury, concerns about the impact of the spending squeeze are made plain.
And it's no secret that the Home Office budget is one of the departments in Whitehall that is not protected from the overall cuts.
But in the aftermath of the Paris attacks, political concern over policing numbers has become acute.
Former counter-terror policeman Kevin Hurley, now Police and Crime Commissioner for Surrey, warned that police responding to a terror attack outside London would be overwhelmed.
He told the BBC: "The people would be massacred. The first responding police would also be massacred.
"And eventually we would mobilise sufficient assets from the police but with major military support."
Police officers only have single shot weapons and would be outgunned by people with automatic weapons like the AK-47, he claimed.
The letter to the home secretary was copied to the Treasury, Number 10 and the security services.
It is understood to have been requested at a meeting of the government's emergency committee, Cobra, on the day after the 13 November Paris attacks that killed 129 people.
The BBC has seen key paragraphs of the document, Implications of the Paris Attack for UK Police Preparedness.
It suggests further cuts to police budgets would affect the authorities' ability to respond to multiple attacks.
Steve White, chairman of the Police Federation of England and Wales, told BBC Radio 4's Today programme: "We can barely cope now.
"If there are going to be further cuts to the police service, quite frankly, God help us. We are not going to be able to respond to something on the scale of Paris."
'Flow of intelligence'
The letter cites worries over "surge capacity" - the need to mobilise large numbers of officers and resources in the event of a serious attack.
It says: "It would be remiss of me not to highlight the impact further reductions in police force numbers would have on our ability to manage terrorist incidents of this magnitude, particularly if spread simultaneously across a number of geographical locations.
"Police forces across England and Wales have already seen a reduction of 40,000 officers and further losses will severely impact our surge capacity, which is heavily geared and will reduce very significantly across the country unless a different funding settlement is found."
Speaking on the BBC's Question Time, Mr Burnham said cuts of 5% to the police budget over the next five years were "doable" and between 5% and 10% would be "difficult".
He added: "But go beyond 10%, it's dangerous."
Lord Reid, former Labour Home Secretary, told BBC Radio 4's Today programme: "Cut police on the ground, and you cut the flow of intelligence which is vital for counter-terrorism."
He claimed the "whole police force" could be cut to 115,000 if the cuts go through - saying that same number was deployed in Paris last week.
The most recent figures show there are 124,264 police officers in England and Wales, not including police and community support officers, 6,780 in Northern Ireland and 17,261 in Scotland - a total of 148,305.