If you are happy with aami, I would speak to them. If you have a quote for a cheaper price, a lot of companies offer to match it or sometimes better it.

I did a bit of shopping around when we got our renewal notice (I pay annually). I couldn't get close to what we are paying for H&C with Budget. I've never had to claim anything yet but when I've rang for other things, the service has been great. We have H&C and two cars with them.