Most insurance companies manage to successfully issue an insurance certificate and take your premium off you
, the real test is of course if you were unfortunate enough to have an accident.
Presume you've not had to put Sheila's Wheels to that particular test over the past few years?
You could try ringing them to ask if they could match or come close to the AA quote, although I have to say I did take up M&S insurance's offer to do just that a few years ago, and after talking me through every single detail again...
...they came up with exactly the same premium and wouldn't budge a penny!
My rough rule of thumb is that I can't be bothered to change companies for the sake of up to £20, but over that I'd probably jump ship, so in your case I'd try for a reduction first, and if no joy, jump ship.