Excellent! Six digits worked fine.
FYI for anyone else hoping to email them, I found an old email address I'd used and got this annoying autoresponse:
Thank you for contacting Heathrow Rewards. This address is no longer monitored for new enquiries, please contact us online.
If you are contacting us to advise of a missing purchase, please login to your account and complete the webform that is available under 'Contact Us' on the 'My Account' page.
Kind regards,
Heathrow Rewards