Police authorities across the East have warned they are facing a shortfall of more than £10m in force budgets.
A survey by BBC News Interactive has found that Hertfordshire Police could need to make savings of £4.6m, while Norfolk needs an extra £2m.
Police authorities say despite the shortfalls they are still committed to neighbourhood and front-line policing.
The Home Office said the government had invested heavily in the police to achieve national policing priorities.
Peter Conniff, chairman of Bedfordshire Police Authority, said the increase in its grant, though larger than those received by many other authorities, still "fell short of what is required".
Police force grants this year (% increase compared to 2005/2006)
Beds £64m (up 4%)
Cambs £73.8 (up 3.3%)
Essex £162.7m (up 3.2%)
Herts £110.4m (up 3.3%)
Norfolk £80.5m (up 4.3%)
Northants £68.7m (up 3.2%)
Suffolk £65.3 (up 3.2%)
Thames Valley £218m (up 3.3%)
"We have a shortfall of about £1.5m - that's a substantial amount to look for when trying to maintain services," he said.
He said the authority was "determined to maintain front-line policing", so any potential cuts would hit other areas."
Stephen Bett, chairman of Norfolk Police Authority, said its £80.5m settlement fell short of what was needed by £2m.
"It does make our lives extremely difficult. We will have to look closely at the figures," he said.
Essex Police Authority chairman Robert Chambers said it looked like the county's 3.2% would "just about cover our costs. It's a standstill budget. We wanted 4.5%."
David Wood, vice-chairman of the Suffolk Police Authority, said this year's £65.3m grant fell about £1.3m below what the authority had been hoping for.
"It won't have a dramatic affect on front-line policing, but we will have to look at how we operate across other areas," he said.
He added: "The government keeps bringing in initiatives, but let's have the money to do them properly."
Dr Marie Dickie, chairman of Northamptonshire Police Authority, said she had concerns over the 3.2% increase.
She said Northamptonshire Police has over the past five years been annually underfunded to the tune of £2m.
'Not easy settlement'
Ian Laidlaw Dickson, chairman of the Hertfordshire Police Authority, said the force's £110.4m grant fell about £4.6m short of what they had been looking for.
"It is not an easy settlement. We are getting squeezed. We now have to try and work out where we go with this, " he said.
He said the force was committed to pushing forward neighbourhood policing.
Cambridgeshire Police Authority chairman Michael Williamson said due to complexities of the grant he did not want to comment at this stage.
A Home Office spokesman said the above inflation increase in funding for the police would help "maintain record levels of policing".