Even with the police agreeing with your version, if there were injuries involved, establishing the extent of the injuries can take time. The insurer will need to understand the long term affects of any injuries you sustained and it is in your interests to let them do so.
This is not to say, they can drag it out for ever and a day. Stay persistent but remain calm. You will achieve nothing by antagonising those very people that decide on the amount of any settlement.
Where injuries are involved, it is prudent to seek legal advice.
Many insurers now include the option of including such cover at renewal but for others, you may need to sign some kind of declaration with the legal advisor that agrees to take your case on whereupon, you agree to reimburse their costs if they do not succeed or cannot recover all of their fees from the other person’s insurance company on winning the case for you.
There are also an abundance of solicitors that will take on cases on a no win, no fee basis, but again, make sure you understand the arrangement before signing up to it.
Hopefully, if you are unfortunate enough to be involved in a non-fault accident, it is resolved before your insurance policy is next due for renewal otherwise your no claims bonus could be affected until the matter is resolved.
Don’t lose heart however as your insurer will reimburse your NCB and any surplus premium you paid at renewal when/if the claim is resolved in your favour.