Ebbie.
Not sure of the legality of owners renting out N reg in the UK. Virtually all of them are for personal or equity group owner use.
You can fly G reg on your FAA licence but there are now some hoops to jump through before you can, including two written exams and license verification via official forms to and from the CAA / FAA.
I hope your visit is far enough in the future to allow completion of the above.