When the first AHRC Research Centres were founded in 1999, it was on the understanding that funding was for a maximum of five years, after which the Council’s grant would cease and the strategy for continued activity after the AHRC’s period of funding built into each Centre’s strategic plan would come into effect. The principle that existing Centres should not benefit from continuation funding remains AHRC policy. However, following its evaluation of the Research Centres scheme in 2003/4, the Council agreed to consider further selective investment in Research Centres by means of what is termed ‘Phase 2 funding’. This is not intended simply to continue or further an existing Centre's prospectus and profile of activities, but aims to encourage Centres to develop different, more ambitious and coherent programmes and objectives. Central to the objectives of Phase 2 funding is the achievement of what is often described as world-class research and the fulfilment of a leadership role at national and international levels.

Initially, the Arts and Humanities Research Council invited applications for Phase 2 funding from the ten AHRC Research Centres established as a result of the 1999 competition, and a further round of bidding allowed the remaining nine AHRC Research Centres established as a result of the 2001 and 2002 competition to apply for funding. Two AHRC Research Centres were awarded Phase 2 funding from each round: in 2004, the Centre for Irish and Scottish Studies and the Centre for the Evolution of Cultural Diversity; and in 2006 the Centre for Studies in Intellectual Property and Technology Law as well as the Centre for Musical Performance as Creative Practice. In each case Phase 2 was made available for up to five years, from the end of the original AHRC Research Centre’s funding period.

CMPCP’s own budget is approximately £2.1 million, with an AHRC grant of over £1.7 million and contributions of c. £430,000 from the lead participating institutions – the University of Cambridge, King's College London, the University of Oxford and Royal Holloway, University of London.