I changed my house insurance from Saga to Tesco 2 years ago. Tesco gave me around half the Saga premium and didn't put it up hardly anything the second year. My Saga Car insurance has risen a small amount each year but is still reasonable at the moment. Pet insurance goes up regularly but as Kitty is getting old (he's 14) its hard to get it any cheaper.
My breakdown insurance comes as an inclusion with my Nissan annual service.