Transponder shmansponder. It's illegal to do aeros over a 'congested area' at any height.
The Rules of the Air Regulations 2007, Shedule 1, Section 4, para 15:
Aerobatic manoeuvres
15. An aircraft shall not carry out any aerobatic manoeuvre—
(a)over the congested area of any city, town or settlement; or
(b)within controlled airspace except with the consent of the appropriate air traffic control unit.
Course it all depends on how congested Hook End is, no-one's suggesting every house has to be avoided. But the person who told your Dad 'the transponder was checked' deserves a slap. I'd give the airfield manager a ring and explain the situation.