Liberal Democrat controlled Somerset CC set a budget£3.4m above cap in March. The county wrote to Mr Prescott on Tuesday to request an early meeting with him and his civil servants.
In his letter, Somerset leader Chris Clarke said: 'I appreciate that Somerset is not alone in suffering cuts, but during the past four years we have seen the loss of 300 teaching posts, 400 school assistants and several hundred other staff. The previous government allowed us the third lowest standard spending assessment for education of all the counties and the lowest budget settlement of any county for 1997-98.'
Mr Clarke said that while the county accepted that some cuts were inevitable, it had decided to protect specifically 125 care home places and 90 teachers.
All three main parties on hung Oxfordshire CC agreed to set a budget£6m above cap. The county, which saw the Conservatives replace Labour as the largest single party following last week's county elections, has yet to decide how it will handle an appeal to Mr Prescott. The council meets on Tuesday.
But an Oxfordshire CC spokeswoman said: 'The feeling is that this government has put education at the top of its agenda. Now where's the money to pay for it?'
Warwickshire CC bust its cap by£2m but has similarly made no moves to contact the deputy prime minister.
Outgoing environment secretary John Gummer announced last month that all capping decisions would be held over until after the general election, so the capping limits for all three counties remain provisional.
An appeals process will only be triggered if Mr Prescott decides to enforce the provisional spending limits.