There's a dedicated number for Avios Plus cards -
0800 161 5309.
I called and got through after only 30 seconds of holding. The agent said they'd received a memo this morning advising of a supply issue with the new cards, and to reassure any customers who call up that cards will be sent out ASAP. I asked how long approximately, and she said "the memo doesn't indicate how big the delay is - sorry I can't advise how much longer it will be". Gave my account number and she was able to confirm that a card number WAS generated/issued on the 6th March, but the card not been printed yet due to supply issues.
Tick tock...