An "English clause" is a contractual provision requiring a buyer to report any better offer to his supplier and allowing him to accept such offer only when the supplier does not match it. An "English clause" is a vertical restraint

Vertical restraints

Vertical restraints are competition restrictions in agreements between firms or individuals at different levels of the production and distribution process. Vertical restraints are to be distinguished from so-called “horizontal restraints,” which are found in agreements between horizontal competitors...

 under competition law

Competition law

Competition law, known in the United States as antitrust law, is law that promotes or maintains market competition by regulating anti-competitive conduct by companies....

, and can be expected to have the same effect as a single branding obligation, especially when the buyer has to reveal who makes the better offer.