So you may want to know the laws on bike racks for the UK
There is no specific law on bike racks, but you can find it all in
The Motor Vehicles (Construction and Use) Regulations 1986 (?) as amended usually referred to as ‘con and use regs’
and the Motor Vehicles (Lighting) Regulations 1999 (?)
There is a section about needing a back number plate is in the Registration and Licensing regs (can’t even stab at the date.)
Con and use cover things like dangerous parts, insecure load.
Lighting regs., cover lighting
Licensing reg., cover number plate details, including angles of visibility.
The easiest way to get the exact wording of these regulations apart from the internet would be a copy of Stone’s Justices’ Manual, a huge tome, published annually in several encyclopedia size volumes. Be warned, unless you know to interpret regulations, it is a daunting task.