The problem with changing from one insurance company to another is that the new company will not cover any pre-existing conditions.
So, using my older Cocker William as an example - William was diagnosed with lumbosacral disc damage 4 years ago and has a lifelong eye condition called Dry Eye. Diagnosis of the disc problem involved a MRI scan that cost over £1,000. He hasn't yet needed surgery (and I really hope never will) but has acupuncture every 8 weeks costing £40 per session and has had other therapies in the past too. Dry Eye requires daily eye ointment and 6 monthly check ups, average cost per year £200. I can claim all of those with my current insurers because William has lifetime cover.
But if I were to change insurers he wouldn't be covered for any of the above or any future treatments relating to those conditions.
My younger Cocker is with the same insurers and I've never made a claim from them for him, so I could change if I wanted to. But the new insurer would want me to declare any illnesses he's had, and would probably check with my vet. He had conjunctivitis once and his anal glands emptied once or twice. Some insurers would accept those as minor and not consider them to be pre-existing conditions, but some would even exclude minor conditions and illnesses such as those.
So my advice would be to choose very carefully and make sure the policy you choose is a lifetime one and not one that pays up to a set amount for each condition and then stops paying.