Non fault claim-how to deal directly with third party insura

[stinkyspanner]

So yesterday my car was hit whilst I parked (and i was sitting in it) by another vehicle which the driver had also parked but forgot to put the handbrake on. His car rolled backwards and scraped down the side of mine damaging the rear door and quarter panel.
Obviously I have to inform my insurer but if possible I'd like to deal directly with the third party insurer and remove the 'accident management' people from the equation.
Anyone know how I can do that? It seems like as soon as I inform my own insurance the wheels are set in motion for their accident management co. to take over which I'd rather not happen as they were useless last time..
Presumably it's in the third party insurers interest to deal directly with me so they don't get rinsed for credit hire etc, but I'm not sure how to get to that point

[zarjaz1991]

You don’t have to use the accident management company if you don’t want to.