Any large organisation or even individual (both civil and MOD) can "self-insure" ie. become an insurer. Some sort of bond is lodged with the central insurance regulators to ensure that the liquid funds are available to cover a large 3rd party claim.
Tescos do it for their fleet and premises (and they suffer on average two total store losses a year - burn down etc.). When I worked for ICL they did it.
And the MOD can supply you with a letter stating the cover they provide in the absence of a proper insurance certificate.
Insurance is a form of betting and the insurance companies have spent a fortune on employing great expertise to determine the likelyhood of claims and setting the premiums to ensure that they make money. Therefore, as a consumer, the odds are against you claiming - which if its good enough for the insurance companies is also good enough for me - go for the minimum insurance required to comply with the law.