HM Inspector of Constabulary Zoe Billingham said the overall response to the financial challenge by police forces had been "good".
But she added: "We have found a considerable variation in the approaches taken by forces - and in some cases this leaves us with concerns about how some forces will manage in the face of further cuts.
"We also have some concerns that neighbourhood policing risks being eroded as forces change how they deliver local policing.
"We flag as a risk the potential that, as a result of these changes, there will be fewer visible police officers with a warrant card, with the power of arrest, out on our streets when they need to be.
"Neighbourhood policing is the cornerstone of the British policing model - not a 'nice to have'."
More top news
A Finnish punk band whose members have autism and Down's Syndrome have been chosen as the country's entry for the Eurovision Song Contest.
The PM promises to double to 200,000 the number of homes built under an existing scheme aimed at easing Britain's housing shortage.
The Met Office has weather warnings in place for snow and ice until 10am in the north and west.