The United Kingdom is a highly open economy, and has a monetary policy strategy of targeting inflation in consumer prices. In this paper, we look at the evidence from the UK on inflation behaviour, and examine the propositions from several theoretical models about inflation dynamics in an open economy, focussing in particular on the hypothesised connections between the exchange rate and consumer price inflation. Theoretical open-economy macroeconomic models cover the waterfront on this issue, ranging from exchange rate disconnect to a rigid link between nominal exchange rate changes and inflation. We estimate on UK data the open-economy Phillips curves implied by the alternative explanations. We argue that, of the alternatives considered, only a model where imports are modelled as an intermediate good, as in McCallum and Nelson (1999), provides a reasonable match with the data. Unlike the standard model, in which imports are treated as a final consumer good, the intermediate-goods specification provides support for a policy of CPI inflation targeting.