Some of the high-end homebuilts such as Lancairs have been built in the US with turbines, and I 'm sure I've seen mention of one in the UK. If so dunno if it's on a PFA permit!
Also saw a Rotax (?) powered highwinged thingummybob this morning - as Fox Alpha says, very quiet and fairly nippy and sounded a bit like a turbine. Might have been a Glastar?