From the Wikipedia page 
Peterborough City Council is the local authority for Peterborough in the East of England. It is a unitary authority, having the powers of a non-metropolitan county and district council combined. The City was incorporated as a municipal borough in 1874; from 1888, it fell within the jurisdiction of the Soke of Peterborough county council and from 1965, Huntingdon and Peterborough county council. In 1974, it was replaced by a wholly new non-metropolitan district, broadly corresponding to the Soke, in the new enlarged Cambridgeshire. In 1998, Peterborough became independent of Cambridgeshire as a unitary authority, but the city continues to form part of that county for ceremonial purposes as defined by the Lieutenancies Act 1997.
The leader and cabinet model of decision-making was adopted by the city council in 2001. The Conservative Party held control of the council from 2002 until 2014, when it became no overall control. It is a member of the East of England Local Government Association.