The home secretary, Theresa May, has dismissed fears that deep spending cuts could undermine the ability of the police to tackle possible civil unrest, and insisted the British did not respond to austerity by rioting on the streets.

May told the police superintendents' annual conference that it was "ridiculous" to suggest savings could not be made in policing, and went on to challenge the political orthodoxy that fewer officers would inevitably mean more crime. The home secretary pointed out that around the world significant falls in crime had happened alongside stable or even falling police numbers.

May was responding to a warning from the Superintendents' Association president, Derek Barnett, that severe spending cuts could undermine their ability to cope with rising social and industrial tensions as a result of the government's austerity package. Her speech also follows alarming predictions from the Police Federation that up to 40,000 police staff jobs could be lost as a result of a 25% cut, opening the way for a "Christmas for criminals".

May told the police: "The British public don't simply resort to violent unrest in the face of challenging economic circumstances. We must have a rational and reasonable debate about policing. Your association has a long and proud history of constructive and sensible contributions to policing policy-making – long may it continue."

She said it was important to pre-judge the outcome of the spending review to be announced on 20 October: "Budgets will be tight across the whole of the public sector but is just pure speculation to start guessing at the final settlement.

"I will work hard to ensure a fair deal for policing but there will, most definitely, need to be savings made. It is ridiculous to suggest that there are not savings that can be made in policing. And lower budgets do not automatically have to mean lower police numbers," she said, adding that procurement, operational support and back office roles rather than the frontline would be first in line for cuts.

The home secretary tried to reassure the police that the cuts, to be agreed over the next few weeks, would be achievable and would not be imposed overnight.

"You will have an entire five-year parliament over which to make these changes happen but you must make them happen. Her Majesty's Inspectorate of Constabulary have said that £1bn could be saved without reducing police availability. In this economic environment, I am clear that the police service can make savings by finding new and more cost-effective ways to do business."

She said there were more police officers than ever before – 142,000 in England and Wales – but that perceptions of crime had never been higher.

"But in many forces in the UK and in many countries around the world, we have seen significant reductions in crime alongside stable or even falling police numbers. Look at the example of the New York police department where they have managed to cut crime at the same time as reducing the number of officers from 41,000 to 35,000."

May said management and leadership was more important in determining the effectiveness of a police force than the absolute number of officers.