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
The cold weather is set to continue over the next few days with further wintry showers and icy patches, particularly at night.
Some child abuse survivors say they received death threats after MPs published their details online.
Coronation Street has found another actress to play Bethany Platt, after a previous one was dropped for lying about her age.