As the rules presently stand; Assuming that the April 2017 deadline is extended to April 2019 (which I have no real source confirming either way) [
http://www.peter2000.co.uk/aviation/easa/] - if you can find an N-reg plane in the UK, you should be able to rent it completely legally with an FAA certificate.
If April 2017 deadline goes ahead, then as of April 2017, it will depend where the N-reg is based, if it is in the UK, you will need both EASA licence AND FAA certificate to fly the aeroplane in UK airspace. Funnily enough however, if the aeroplane is based in the UK, but you rent it from another EU country (ie: France), technically you only require the FAA certificate providing that you don't fly in UK airspace. Oddly enough - but irrespective of the question, an N-reg based in the UK can be flown in UK airspace, with a UK issued EASA licence.
(ps: anyone who has more information may contradict me, but I did spend considerable time looking at purchasing an N-reg in early Jan)