Switching Barclaycards

Stompa

With the demise of the GE Money Everyday card I'm looking for a new cashback card. The Barclaycard offering looks pretty good, but is for new customers only - and unfortunately I've had a Barclaycard since 1978! (though only used about once a year these days).

Has anybody ever had any success in persuading Barclaycard to switch an existing card to another type (in this case to the cashback offer)? Or do they rigidly stick to their 'for new customers only' rules?

Thanks