Despite uk.gov wanting to treat anyone filming or taking pics on the street as a terrorist recon unit, it is not illegal here. Also no need for a Helmet cam, just a cheap micro DV from Hong Kong
Mount it in your car and you get vids like this (EDIT - this is not me, just a random vid I found on youtube taken with this type of cheap camera)
I would suspect Mr Plod would not like to be filmed by someone else throughout his arrest. If you happened to pass him when he has stopped someone then thats in public anyway.
At least thats the position here.