Why don't you try gather up the better quotes and go back to your insurer with them, see if they'll better them?
If its any help, I recently cancelled a mortgage repayment protection policy which we were paying monthly - got a refund of about half a months payment back from the insurer cos I cancelled mid-month. You're most likely paying for the month in advance if you're paying monthly, so would be refunded from when the cancellation was effected.