Can't be absolutely certain, but if you want to fly a G-registered aircraft, you will need a JAA licence.
There have been occasions in the past where airlines have "sponsored" foreign pilots with non-JAA (or in those days, UK) licences, and they have operated under a dispensation from the CAA, but I'm pretty sure that all came to an end when British Midland imported a bunch of Aussies and the CAA jumped on them. As I recall, the BM guys were given 9 months to get a JAA licence or they had to go. However, that was probably a "special case" and I doubt that they would do it again. Could be wrong, though, flybe may have done some sort of deal with the CAA.
If you want to fly on this side of the pond, try the Irish, they will happily take a FAA licence - as in a whole bunch of Mesaba pilots that Cityjet took on, all with FAA licences...