They can do this for eleven years?!? Is this an agreement reciprocated between the US AND UK?
Under the rules, a Brit could enter for a three month period without a visa. It is non-extendable. If the Brit were to leave the country, he could return for another three months, etc...
Theoretically this could go on forever. The only restriction is no residence / employment.
The agreement is/was reciprocal (you don't need a visa to travel to Europe, unless you want to work).