I phoned the 0345 number on Wednesday 19th and was told the change could happen along the lines you explained. With the statement date being the 20th I was told to phone back on Friday the 21st. Today (21st) I was told on the 0345 number that the dates available didn't change, I remarked I had changed dates on Tesco CC's to different dates before and said that it was linked to the statement date. I was told that was no longer the case. I was advised to pay by phone on the 14th of the month which would meet my requirements (what). I then asked to cancel the card as I would re-apply until I got a date that worked. I was told to cancel online. My wife's Tesco CC is debited on the 14th so feel this may well be some sort of sexual discrimination.
Perhaps easiest if you can tell me the best date to phone given the above statement date to get this changed so I am debited on (obvs some months shortly after) the 14th as I am not making payments with the card at present so multiple monthly payments aren't an issue.