In recent years questions concerning the impact of public research funding have become the preeminent site at which struggles over the meanings and value of science are played out. In this paper we explore the 'politics of impact' in contemporary UK science and research policy and, in particular, detail the ways in which UK research councils have responded to and reframed recent calls for the quantitative measurement of research impacts. Operating as 'boundary organisations' research councils are embroiled in what might be characterised as the 'politics of demarcation' in which competing understandings of the cultural values of science are traded, exchanged and contested. In this paper we focus on the way the UK's 'Engineering and Physical Sciences Research Council' (EPSRC) has responded to contemporary policy discourses concerning the impacts of public research expenditure. We argue that, in response to the shifting terms of contemporary science policy, the EPSRC has adopted three distinct strategies. Firstly, in collaboration with other research councils the EPSRC have emphasised the intellectual and metrological challenge presented by attempts to quantify the economic impact of public research expenditure, emphasising instead the cumulative impacts of a broad portfolio of 'basic science'. Secondly, the EPSRC has sought to widen the discursive meaning of research impacts - specifically to include societal and policy impacts in addition to economic ones. Thirdly, the EPSRC has introduced a new framing into the 'impact agenda', preferring to talk about 'pathways to impact' rather than research impacts per se. In responding to government priority setting, we argue that the EPSRC has sought to exploit both the technical fragility of auditing techniques and the discursive ambiguity of notions of impact. [ABSTRACT FROM AUTHOR]