According to my solicitors, a non fault should not affect my insurance, they reckon this is not claimable, which is obviously b*ll*cks.
b*ll*cks on both counts (at least they have a full set of b*ll*cks).
You are entitled to be put back inot the same financial position had the accident not happened.
This can be added to your uninsured losses.
The only stumbling block might be if you've signed something in "full and final" settlement.
Otherwise add it on to your claim.

Of course you will have to provide proof that the increase is solely a result of the non-fault claim but that shouldn't be hard. Quote with and quote without should be simple enough.