None. These are two separate pieces of legislation.
The building regulations set out a series of performance standards which building work should achieve and the process for ensuring compliance with those requirements. They are enforced by the relevant building control body.
The Party Wall etc Act 1996 provides a framework for preventing and resolving disputes in relation to party walls, boundary walls and excavations near neighbouring buildings. Responsibility for ensuring compliance rests with the building owner who wishes to carry out the work. Failure to follow the procedures laid down in the Act is a civil matter for the relevant parties.