I'm pleased to tell you that's wrong. I can't post a URL but Google for "CAA Recognition of ICAO third country licences in UK airspace". I have recently been through this process and the CAA officially confirmed that I can fly 28 days a year non-commercial VFR day time with my FAA license (there was a small fee and I had to do an acclimatisation flight). Now I'm wondering which other countries offer something similar. The only other one I found was Germany but I haven't tried it yet.
Zvi