Point of data - I've been looking to move to a lower-fee card, and so rang Virgin Money twice over the past month to discuss cancelling my card. As per the new regs, I was offered no sweeteners of anything being waived, even when I said that the high annual fee was the reason I was thinking to close. When they mentioned the current month's points wouldn't be swept over, I said I'd wait to the end of the month and call again to close.
I rang again today, ready to close it, but phrased a bit differently with success: they waived the $289 annual fee for this year.
The phrasing I used this time was: "I'm considering closing the account because the annual fee is high. I notice that you have a promo with another card of a $50 annual fee for life for new customers, so could you offer something like that to make it more worthwhile for me?" They transferred me to someone else who then offered me a "once-off" annual fee waiver.