Yes,
You can fly an N-reg in the UK on your UK JAA licence - no problem. However, the FAA rule that allows this broadly says
'you must have a licence issued by the country you are flying in or an FAA licence.'
One can debate if a JAA licence is issued by the country Europe or by one of the individual states. A conservative view of the law would say, with a UK JAA licence you can only fly in the UK. A more aggressive view would be, it is a JAA licence and you can therefore fly in any JAA state.
If you would like to read hundreds of posts debating both sides of this view a quick search will drag them up - the summary is, no example has ever been produced of someone charged with operating an N-reg with the 'wrong state' JAA licence and either been found guilty or not guilty - So we don't have an answer if the aggressive stance is correct.
In addition, there are various proposals with regard to the licencing of flight crews for foreign registered aircraft that are in drafting and will come into force in 2012 or later.
If you ever have occassion to go to the US you can, through a fairly simple (but longish leadtime) process, get an FAA licence based on your JAA one.