If the ring is insured for it's current value either under an allowed single article limit or as a specified item and the policy offers new for old cover, then it will be insured for the current value, not the purchase value - unless otherwise stated in the policy. You tend to find that most of the reputable companies will pay the full value. If you bought insurance on the cheap because it saved loads through compare the fat opera guy or whatever, then it might be more of a battle, as typically all those unheard of companies are cheap for a reason.
The biggest issue is that most insurers pay out in vouchers for jewellery items via their specified supplier, which is usually one of those ghastly high street chains.
For a ring of this value, of course it is worth claiming. That's what you pay your insurance for. Yes the premium might go up next year, but not to the value of having to replace an £1800 ring like for like.