Sorry, what do you mean it's not for the police to apportion blame? Whilst I accept we don't play judge and jury, it's a basic police function to investigate collisions and it's something we've become exceptionally poor and very lazy at.
To the OP - this isn't the sole responsibility of a solicitor and/or your insurance company, although the latter will be able to give you really sound advice.
If you're not happy that this has been properly investigated (and in the circumstances as described I wouldn't be) then you need to take it further. There will be an admin function somewhere within every police force where collisions are recorded - the first thing to do is ask what investigation has taken place.