Highways Agency are very separate to police - but you've pretty much hit the nail on the head about what their Traffic Officers do, they shepherd traffic at incidents and remove the bricks / glass / animal carcasses / broken down cars (if they can be dragged with a 4x4 and if there was no criminality or serious injuries) until Police have done their bit, if they are needed. Unless, of course, you'd prefer to have much more highly-paid, highly-trained police doing these less glamorous tasks?
I'd rather have them out there nicking members of the Centre Lane Owners Group, or mobile-phone-using drivers, or people who think that car maintenance is optional...
If anyone wants to come along to our control centre in Godstone, which runs the southern half of the M25 and all the motorways and trunk roads down to the Coast as far as Dorset, just yell and I'll see if I can arrange something!