Only issues with changing insurance providers is that any new company will not take on an existing condition, so if you need to claim in the future for something that is connected to what you have just claimed for you will not be covered.
I used to hold pet ins with E & L and my first claim with them they refused to pay, took them to insurance ombudsmen, they then paid out. Changed my insurer, which meant not covered for the ongoing skin complaint just paid by E & L.
Pet insurers have you by the short n curlies!