They can i have personal experience of this i had a Thai insurance policy linked to my visa (so a well known company), after a small claim that they tried to wriggle out of (my doctor phoned them), then 3 months before my renewal. my hospital emailed me to say the insurance company wanted to see my medical records, i agreed. Then at renewal not only had my policy gone up 80%, they they added a load of exclusions for things i did not have and still don't have, it was as if they were looking at someone elses
medical records, i phoned them and they just said you have gone up a band as for the exclusions they would say nothing, my claim was for burnt tissue, a foot spa put neat acid on my feet despite me warning them, of course they had no 3rd party liability,
I did consider phoning the regulator, but thought the insurance company would simply refuse to pay out on any claims