It can be really straight forward weenie. Glad to hear you are OK.
I know that you shouldn't admit liability but not doing so when there could be no other explanation is hard. Be very upfront with your insurers, and I am sure that they will not penalise you for just being honest. A guy drove straight into the back of us when we were stopped at traffic lights. He too admitted liability and we were surprised by how quickly the claim was resolved by his insurers, I guess because there no counter arguments to delay things. You Have no claims discount but if your insurance is a lot higher next year then stand by to gasp out loud when you see the results of quotes from other insures.