I recently had to make a first claim for my cat after she developed hyperthyroidism. She had an operation but then had to be referred to a different vet overnight as she needed oxygen because she became so distressed. I put claims into both vets and waited, knowing with insurance its sometimes hit or miss. Also I'd read reviews where people waited months. Anyway after 3 weeks I received letters saying both insurance claims were being paid. No hassles or issues. A great relief to me because if it hadn't gone through I would have had hundreds of pounds to pay somehow.
Like I said, I know insurances are sometimes a minefield but all I can say about Tesco is that for me (and Molly my cat!) they came up trumps.