Having instructed on 'N' reg aircraft, both in the UK and the USA, both for licences and type ratings and having dealt extensively with the DETR and the CAA on the matter, my information is NO - you may not, legally, instruct on an 'N' registered aircraft in UK airspace without the appropriate FAA certification.
My information is that, irrespective of whether you are remunerated or not, flight instruction is considered, in law, as aerial work.
Whether you prefer to accept my opinion or Noggin's, I would strongly advise that you consult both the CAA and the company that insures the aircraft to ensure that you don't end up with a personal liability for some tens of thousands of pounds should anything go wrong.