The Rules concerned originate in the Schengen Treaty of June 14th 1985 which are incorporated into the Law of all signatory states.
Generally, the Treaty permits the residents of implementing countries to travel between Schegen countries without border checks. This would ordinarily exclude Brits, however, Schengen is also extended to cover those who by way of visa or other rights have the freedom to reside within a Schengen country. A UK Citizen, therefore, once within a Schengen country, has the same rights to move freely between Schengen countries without border checks.
2D