Britain's most senior anti-terror officer John Yates has sparked a political row after he warned spending cuts would increase the risk of attack.
Cabinet Office Minister Francis Maude reacted angrily to Assistant Commissioner Yates's comments, accusing him of "shroud-waving" and "alarmism".
But Labour's Alan Johnson warned "we will all be in greater peril" if anti-terror operations are scaled back.
The Times said Mr Yates described the planned cuts as "eye-watering".
He claimed cutting 25% from the police budget - in line with across-the-board cuts to departmental funding announced in last month's Budget - risked weakening the nation's defences against al-Qaeda, the newspaper reports.
'Driving down costs'
He was reported to have made the comments at a private meeting during the Association of Chief Police Officers (Acpo) annual conference in Manchester on Thursday.
Mr Yates was said to have told the meeting the Metropolitan Police (Met) would see £87m wiped from its anti-terror budget, while units across the country would lose £62m.
Cabinet Office Minister Francis Maude - the man David Cameron has put in charge of shaking up Whitehall and ensuring greater accountability from public servants - warned Mr Yates against "alarming" the public.
He told the BBC News channel: "I'd like to avoid public servants doing this kind of shroud-waving in public.
"There is a special responsibility on all public servants to be really careful what we say and what we do.
"It's going to be pretty important for people who are managing big public services like police forces to focus on cutting out unnecessary costs, driving down costs, being as efficient as they possibly can before they even begin to contemplate talking about alarming the public in this kind of way."
But Mr Yates's words were seized on by shadow home secretary Alan Johnson, who said they were a sign that "this government doesn't consider policing and counter-terrorism as a priority".
He said that if these two areas were not ringfenced as they had been when he was in charge at the Home Office "you will diminish the number of police officers, you will seriously affect our ability to counter terrorism".
At a time when the UK was on "severe alert" of a terror attack, the "public now understand that their streets will be less safe if these measures are introduced".
He vowed Labour would oppose any cuts to anti-terror police budgets in the Commons, claiming "this is a government that is as soft as a damp marshmallow on crime".
Summing up his position, he said: "We will all be in greater peril if we cut back on the ability of the police and the other agencies to defend this country from terrorists."
All government departments - except health and international development which are ringfenced - face real-terms cuts of 25%, Chancellor George Osborne has said.
But they will have to wait until October and the results of the government spending review to find out precisely where the axe will fall.
An Acpo spokesman said police forces had to face cuts in the same way as other areas of public spending.
"The home secretary has made clear that alongside other areas of public spending, policing must deliver its share of savings to meet the fiscal deficit," he said.
"No area of policing is immune."
John Yates is one of Britain's most high-profile police officers who, as head of the Met's specialist crime unit, led investigations into cash-for-peerages allegations and claims newspapers had hacked celebrities' mobile phones.