I don't see how you can avoid this one.
As you know, the FRS avoids you having to account for all the input VAT on goods and services you buy. But the flat rate for your particular type of business is based on an average assessment of what you buy as a proportion of your turnover. Where one ends up out of pocket is when one's purchased services are greater than that assessed by HMRC. This is in essence what has happened here - you've suddenly got a large VAT expense. It is not the insurance company's issue because they are merely seeking to migitate their claim costs by the amount of VAT from you - and you are a VAT-registered business.
There is a scheme for those using FRS for claiming back the VAT from capital purchases over �1000 - you could phone the VAT helpline and see if there is a way of using this - not I suspect not.