You can claim the difference between the cost of insurance in NI compared to Central London. You'll be able to get more information from the Admin Office at TBK.
Some of the usual car insurers will cover NI, but many won't. You may be better going to an NI company.
Quinn Direct are good (and safe for military)
AXA are apparently OK, but refused to quote for my sports car.
The NI equivalent of confused.com is
Its4me 19 out of 20 refused to quote for my car.
I now have a more conventional car, and with Quinn am paying only about £100 more than on the mainland.
Forces Financial's new panel of underwriters may be worth having, but NU is to be avoided - they seem to regularly quote ludicrous figures.
Beware of spurious charges raised by your existing insurer when you move - I am currently in dispute with Tesco Insurance (who don't cover NI), who are trying to charge me a month's instalment +£75 cancellation fee, and I have heard of other companies doing this too. The answer seems to be not to cancel, simply to send them a change of address so that they then say they can't cover you.