OT (ish) car insurance, claims and VAT advice

On the grounds that will be SWK in here:
Back in Feb, a very nice lady wiped the side of the FTO with her X5, left a
note on the screen (well, there was private CCTV in place, so it would
have been dumb not to) and admitted full liability. Given the age of the
FTO and the likely cost of repairs, I hung on until her ins co had
confirmed to mine that they accepted total liability. Good so far. Car was
repaired, my ins co renewed the policy with full NCD and I was happy with
the world. Meantime, it turns out that the repairs STILL haven't billed
to my ins co by the garage for the work - not the first time I've realised
that people in this business have no concept of cash flow (1), but not my
problem.

However, my ins co
keep sending me letters along the lines of 'as you are VAT registered, you
have to pay the garage the VAT on the repair and claim it back'.
Ins co 'think' this may be why its not been billed yet -
confusion at garage. Ho yes, confusion. Question: how can this be? I can
understand if I am liable, but surely garage bills ins co 1 who bill ins
co 2? Excess is waived, complete liability admitted my other party, why do
I have to get involved? It not a big problem if I have to do it, but I
just don't see why / how its relevant? (2)

1: Car written off, third party admitted liability, my ins co 'forgot' to
bill the settlement to other ins co - result was no NCD at next premium
renewal as claim outstanding (3)
2: Yes, car is insured for biz use but then 'nominally', I guess I should
only reclaim the percentage of the VAT etc etc. Nightmare if done properly
3: Resolved through much shoutiness at call centre

 

A quick google produced this.
http://www.theinsurancecentre.co.uk/repair.html
If you are not liable to pay any excess then I don't see how the
question of VAT arises. Even if you did have to contribute you
yourself aren't registered for VAT, are you?

 

Yep, saw that one and came to the same conclusion.

Yep - sole trader, so from a theoretical perspective I only claim fair
business miles allowance on the car, being part private use, hence the
admin nightmare (OK, its so small I wont bother, but its the point of
principle, innit?)

 

A few further down in google was this
http://www.kinghornbodyshop.co.uk/accident.html
which suggests that, if you are VAT- registered, you pay the VAT (and
reclaim it) on the entire cost of repairs, and your ins co just has to
find the amount before VAT. This is, I think, because your ins co
can't reclaim VAT on repairs whereas the policy holder sometimes can.