It's important to know whether you're talking about your own life assurance etc, or the aircraft's and your liability in the case of accident.
For the life insurances etc on your name, there's no other way than to contact all the companies, tell them you've taken up flying light aircraft, and ask them to confirm that the policies are unaffected. In my case, all but one agreed "no change". The exception was my firm's accident policy, which wouldn't cover me for non-scheduled airline flight. I then pointed out that I fly regularly on the company plane, which is non-scheduled. Embarrassed pause, then confirmation that they, too, had me covered.
For liability while piloting, you need to check the policy on the aircraft you're flying. Ask to see a copy. If the club/school doesn't have one to hand, ask them to get a copy for you! Don't wait till you need the cover to find out.
You can never have enough insurance these days, against anything, but I'd say £1 million is the minimum acceptable in aviation, and £10 million probably isn't too much. Just look at the price of a Harrier, and imagine you banged into one by mistake...