The Home Secretary has been accused of failing to take Cambs police's bid for an extra £2m to tackle crime seriously.
Mrs Spence said Cambridgeshire had changed dramatically
Keith Walters, chairman of the Cambs Police Authority, wrote to Home Secretary Jacqui Smith to request the increase to recruit more officers.
Mr Walters said Ms Smith's reply was "dressed up in pretentious language but is words to the effect 'Don't call us we'll call you'".
The Home Office said it could not comment on individual cases.
Mr Walters and Chief Constable of Cambridgeshire Constabulary Julie Spence launched their bid for an extra £2m to recruit 25 new officers every year for the next eight years.
The bid came after Mrs Spence revealed her force needs more staff and resources to cope with the pressures caused by a sudden influx of migrant workers.
In a letter, Mr Walters invited the Home Secretary to visit Cambridgeshire.
"I take exception when I get a letter back from her assistant diary secretary - which is a measure of how seriously she takes me", Mr Walters said.
"I was irritated because I got my answer dressed up in pretentious language, which effectively said: 'Don't call us, we'll call you.'
"In effect it said: 'We are happy to visit Cambridgeshire should the opportunity arise in the future' - despite us having had a whole day of publicity in the national press.
"To receive a response from the assistant diary secretary adds insult to injury."
A spokeswoman for Cambridgeshire Constabulary said Mrs Spence was aware of the letter received by Mr Walters, but declined to comment on its content.
They claim the force is currently understaffed by about 100 officers and the population which the force is required to police is rising steadily.
The growth is largely fuelled by immigration, particularly by economic migrants from Eastern Europe.
Cambridgeshire has one of the country's lowest police officer to resident ratios - 190 officers per 10,000 compared with a national average of 267 officers.
The Home Office confirmed diary secretaries reply to invites on behalf of ministers and secretaries of state.
A Home Office spokeswoman said: "Cambridgeshire Police have received an increase in total government grants of £30 million since 1997/98 and an increase of £22 million since 2000/01.
"Total recorded crime in Cambridgeshire has decreased by 18.7 per cent since 2002/3 to 69,146 in 2006/7 from 85,029 in 2002/3."