Max - the class one is not "the same in every way" as the class two, the difference lies in the standards required to conduct the differing privilages of the medical certificates.
After you've done your initial medical at Gatwick, you can renew the class one with any AME who is qualified to undertake the examination, the CAA's charges for this are fixed and never differ, it's the Doctors bill which often varies significantly - I'd suggest that anyone needing a class one renewal does their homework.