Yes, he will upon entering UK CAA airspace, unless a temporary visitation exemption is available.
This is already the case for loads of other equipment, especially for IFR. Take the old ADF thingy. The CAA requires it for IFR in CAS, but few other countries require it. Germany requires an ADF for some night flight IIRC.
ELT is another. Some countries need it, some don't. All N-reg planes have to carry it, worldwide.
The equipment carriage rules across Europe are an absolute nightmare, and are "obviously" widely flouted without anybody (the pilot in particular) realising.
To date, anybody flying IFR will have been generally aware of the need to carry various bits of variously expensive kit if they want to fly around Europe. Now, with Mode S, attention of VFR pilots is being drawn to it.
One would have thought that JAA would have unified the rules but they haven't. The nature of politics is that local exemptions have to be allowed in order to get anything agreed. EASA, taking over from JAA, is likely to simply force a lot of stuff through.
N-reg owners tend to be more aware of this than most, not least because the rules are more clearly stated.