You should have no charges irrespective of how you claim, I would contact an accident management company or use your legal assistance on your policy if you have it, rather than claim through your insurers. Your no claims bonus should not get affected if you do claim via your own insurers,as long as the other parties insurer has accepted liability. Check your premium after you have advised your own insurer about the incident and see if it goes up. If it does, make sure you claim that increase for the next five years of the at fault party.