if you arent happy with AAMI's response, you ask to speak to a manager, if they say no, ask them they need to inform you of their internal dispute resolution process.
each insurer has this and they have to advise you of this if you are not happy with a situation.
they'll then have 10 days from memory to get back to you.
they have to inform you each part of the process, and if any delays, and expected time frame.
just because they arent your insurer doesnt mean they shouldnt help.
they have taken on a risk and that risk has caused loss/damage to a third party = you. so they should accept if all liability points to it. (I imagine it would as he has legft a note)
with the IDR process, iif by a certain time fram there is no result, then it goes to the EDR (external) and thats where the FOS gets involved as per Terry's post.
good luck with it.