I just stumbled across this and spotted that no-one had replied.
There are different types of GAP insurance, with the most common two being:
Invoice GAP insurance:
In the event of write off (through accident, fire, theft, flood etc) this policy aims to pay the difference between your Motor Insurance payout and the original Invoice Price that you paid for the vehicle when you bought it.
Replacement GAP insurance:
In the event of write off, this policy aims to pay the difference between your Motor Insurance payout and what it would cost, at the time of claim, to replace the vehicle with a brand new version of the same (or nearest equivalent) vehicle - even if that vehicle costs more than you paid for the vehicle originally.
Replacement GAP insurance is superior to Invoice GAP insurance and therefore usually a little more expensive.
There's also a third "Finance GAP insurance" policy which is an inferior type of GAP insurance. Most companies these days have combined their Finance & Invoice GAP insurance policies together (creating a policy that pays the difference between motor insurance payout and the greater of finance settlement figure OR original purchase price) and some companies have combined their Finance, Invoice & Replacement GAP insurance policies to create a policy that accounts for the best of all scenarios.
As a general rule, unless you have a Contract Hire agreement, a Finance GAP insurance policy makes little financial sense given that Invoice GAP insurance (specifically the combined type) is often marginally more expensive and offers superior cover.
Most Motor Dealers only sell Invoice GAP Insurance. Though the number that sell true Replacement GAP insurance are growing. Note that some Motor Dealers have policies that are Invoice GAP insurance policies (as per my descripton above) but they call their product "Vehicle Replacement Insurance" - tricky!
As for the price at £349 for 36 months. That's almost certainly an extortionate price. You can buy online from a range of providers for a fraction of that!
Assuming it's not too late, I hope this helps.
FYI if you did go ahead and buy the dealer's policy at £349, you may well still be within the initial cooling off period within which you can cancel and get a refund. Even if you're outside of the cooling off period, you should still be able to cancel the policy. They may hit you with a cancellation fee, but even after taking that hit, when you've bought a cheaper/better policy elsewhere you'll almost certainly still be left with money in your pocket.