Although not insured with tesco, I too lost a lot of valubles. I can understand the hurt and anger you are feeling. Dont worry, it will get sorted.
My claim came to about K20. Each item was delt with seperatly. I had to provide reciepts or valuations for the items lost. When they offered to replace my watch (a rolex) they wanted to send me a new one through the post. I was not happy with this and asked if I could get it from the same jewelers as my origional one. They would not give me the full value if wanted to do this. (All options are open to you if you ask, and if you dont ask you dont get right?) As we have never claimed before it is only right you ask all questions even if they are silly.
Like the post above they have jewelers on their books who they can get deals with. They also offered me a plastic "credit card type thing" which was loaded up with a value of cash to spend at certain jewelers.
On the bright side, although this was a very upsetting ordeal and I cried like a baby when we got a visit from the loss adjuster. Once I got into the swing of looking around to buy replacements it was so nice choosing something different.
You should not have to pay out first and wait for them to pay you. Kind of defeats the purpose!
Wishing you both well and I hope you find another ring that is just as special as the one you lost. (I even got my new wedding ring blessed at the cathedral I was married at!)
Just food for thought!