Not sure why they wouldn't give you the policy mirror from AXA.
Maybe go back to a branch and specifically ask for them to give you a mirrored policy for a 2nd car - and push for a specific answer if they push back on it?
--> Also, as a plan B... are you named on anyone's policy for any length (spouse, partner, parent, sibling etc)? My brother got out of a hole there in September because he was named on my mum's policy for a couple of years (they once put him on for a few weeks to help him out and forgot to take him off)... He was able to get a letter of NCB as a named driver... which typically counts 50% (so every 2 years as a named driver gives you 1 full year NCB). Made thousands of a difference on his quote as suddenly meant he had 7 years claim free as a named driver. You could if needed then put your Impreza on your main policy (to meet 5 years NCB if not enough via named driver) and put Volvo on the "dearer" policy with less NCB.
Anyhows... Good luck with it.