To reiterate the above .
No it isn't illegal to have a throttle , it must though be a certified throttle by DVLA via test center so a test certificate/V5 is needed ( This is a once in a lifetime certificate) Or it must only operate if one pedals first.
One isn't allowed a twist & go or thumb throttle that is stand alone or a switch , that means any throttle must ceases once one has stopped pedalling.
Currently afaik Wisper is the only EAPC/250W manufacturer that offer the legal throttle route via a test center.
Many though of course do use a throttle that doesn't conform to law so this makes the bike in law a moped as does the illegal motor wattage , typically one will see the deliveroo's and other fast food riders using them ilegally but as they don't bother with complying with road laws like traffic lights, etc,etc then why should an illegal moped bother them.
Aside from all of the above don't expect plod to know the law as at the moment I doubt they do.