Thanks for the reply Elevate (or perhaps 'Demote' would be more appropriate, given the thread!). Interesting, as BA the website states (under the 'i' for Card Expiry Date): "Your card expires one month after your membership year ends, which gives us time to send you your new card".
I'd have imagined you'd at least see the Bronze (or whatever) card being ordered/sent/fulfilled in My Executive Club Items before that date. Or am I missing something?