I'd agree with Scotsgirl on this - my son (5) has had three surgeries on the most basic health insurance (we are with Aviva most basic package you can get) and whilst two were in public hospitals he was done within weeks rather than with a 14 month wait
I would actually cancel my insurance quicker than his (but its not possible I understand to just have a child covered..)
Hold onto your insurance if you can and just move right back to the lowest level of policy you can afford.