01
Do I need extraction in a commercial kitchen?
In practice, yes. A commercial kitchen puts out heat, steam and grease-laden air that has to be taken out mechanically for the room to stay workable and for the grease not to accumulate somewhere it can burn. Under the Regulatory Reform (Fire Safety) Order 2005 the responsible person for the premises has to carry out a fire risk assessment and take reasonable fire precautions.
Not legislation
No law names a specification for a kitchen extract system. DW/172 and TR19 Grease are industry specifications, and any page telling you otherwise has not read them.
Asked for by name
They are what an insurer or an environmental health officer asks for, and a grease-laden extract system is one of the things a fire risk assessment has to account for.
The two specifications are what shows the system was designed and maintained by someone competent, which is reason enough to work to them. What DW172 requires.