I've stayed with the same, NFU, because until the dogs reached 10 years of age the premiums were low for the level of cover and they are one of the few companies that don't expect you to pay a percentage of the bill as well as the excess as dogs grow older. Having said that, I cancelled William's insurance when it was due for renewal last August because at age 14 and having just claimed £4,000 to cover his anal sac removal surgery I decided that I'd be unlikely to put him through anything major (and therefore expensive) again. Over the years, certainly since age 5, I'd always claimed back more than I'd paid out with William.
So now I only have Louis insured with them and I'm awaiting his renewal quote. He's now 10, so I know his excess for new conditions will jump up and the premium will as well because he's lost his no claims bonus! In December last year he achieved the double whammy of a slipped disc in his neck and pancreatitis on the same day, resulting in a tough few weeks for him and me and two claims totalling around £3,200. His monthly premium is £48.74 at the moment, but I think the renewal will be more like £80 per month from what they've told me so far. I'll either go with that or will cancel and take my chance. I think finding a suitable alternative for a 10 year old dog could be tricky given he now has history!
One of the benefits of sticking with NFU has been that some years ago when they, and many other insurers, started pushing up premiums and offering less favourable terms, as an existing customer I was able to keep the terms & conditions I'd signed up to and I was relatively unaffected by the changes in the pet insurance world.
I'm not sure what I would do in future if I were to have another dog. Most insurers offer a lower rate to new customers for the first year and then charge as much as they would for existing customers on renewal. So swapping probably works when no claims have been made and the dog is still quite young, but can back fire as the dog reaches middle age.