Interesting. But the rollout doesn't seem to have reached me.
Under "My Executive Club Menu" > "Your [sic] Executive Club profile" > "Login details" > "Update login details" there is no mention of 2FA; I can only change my password.

Also down the bottom of the page there is a link "Website security" which lists security suggestions and does not mention 2FA, so I guess they don't believe in it themselves :-)

-- edited to add:

Ironically while sending this, BA has just emailed one of my family members saying "it's time to set up two-factor authentication". The email contains a link which generates an error "Too many redirects occurred". Sigh.