This has been covered before but here is a reminder:
Regulation 54 of the Road Vehicles (Construction and Use) Regulations 1986 provides for the fitting and use of an exhaust system including a silencer, to all vehicles propelled by an internal combustion engine.
54(1) Every vehicle propelled by an internal combustion engine shall be fitted with an exhaust system including a silencer and the exhaust gases from the engine shall not escape into the atmosphere without first passing through the silencer.
(2) Every exhaust system and silencer shall be maintained in good and efficient working order and shall not after the date of manufacture be altered so as to increase the noise made by the escape of exhaust gases.
(3) Instead of complying with paragraph (1) a vehicle may comply with Community Directive 77/212, 81/334, 84/372, 84/424 or 92/97 or ECE Regulation 51.02 or, in the case of a motor cycle other than a moped, 78/1015, 87/56 or 89/235.
What this all means is you cannot modify the existing exhaust if it makes it louder than when fitted at the factory, otherwise it will not comply with type approval.
Also, the system will still have to retain the silencers/catalyser where applicable on the original design for that vehicle. Again, modification will mean the system will not be type approved and will not conform to MOT standards.
The simple point is manufacturers spend millions designing a car to meet type approval standards. Once you fit an aftermarket system that is not type approved, or modify an existing system, your system can be illegal.
Check the packaging on the system, and check the part itself for type approval marks. If it has the relevant markings it will be legal, but not if it increases the noise as described in reg 54(2) above.