Trawling through the MIB’s terms, this may be interesting:
“This clause covers various situations. It seeks to reflect MIB’s status as the guarantee body which operates as a safety net for victims who have suffered loss or damage which cannot be recovered elsewhere. It is effectively a final port of call…”
So you can see it does see itself as a last resort.
This is also relevant to your situation:
“In summary, the clause is intended to — • prevent insurers, who have met some or all of the claimant’s losses, from recovering their outlays from MIB; • divert those parts of the claimant’s losses to the insurers who have taken a premium for the risk; • avoid a claimant electing to claim from MIB when there is an insurer who could deal with some or all of the claim MIB does not pay subrogated claims from”
This is pertinent if the lady involved has comprehensive insurance. It says, in effect, that she cannot claim from the MIB but that her insurers should meet her costs. It also prevents insurers from recovering their outlay from the MIB. But of course there is nothing to prevent her insurers from chasing you to recover their outlay (and in fact there is nothing to prevent her from pursuing you herself if she does not want to jeopardise her No Claims Bonus).
In short, the MIB is almost certain to be a non-starter in your case.