At the heart of the matter here is what you intend to do. Period.
If you have aspirations of becoming a commercial pilot or an ATP back in the USA, the FAA and your employer will need for you to compile a 10 year history of all your addresses. If a gap or discrepancy is found, it could lead to problems. Especially if your school transcripts reflect that you were in the UK concurrent to a listed residence in the USA.
In your case it is a judgment call that you will have to make, should you wish to fly professionally in the next several years. You will be required to account for your time overseas--especially if you choose to join the military and/or hold a security clearance. However, since you are a student, your parents' home address should be sufficient as a home of record to report to the FAA--JUST MAKE SURE YOU HAVE DOCUMENTATION TO BACK EVERYTHING UP.
If you do not intend to go any farther than the PPL level, then your plan to use your home address is good-to-go.