Further to Michael's suggestions, the Help page also mentions:
Why am I having difficulty adding, using or changing my debit card?
There could be a number of reasons why you are unable to change your debit card:
You have tickets still to be entered into draws
You have an unfinished Instant Win Game(s)
The balance in your account is too high
You have recently changed your debit card
You have an unclaimed prize waiting to be paid to your debit card
Suggestion: Please access your National Lottery account to check if any of the above may apply and complete any required actions (e.g. finishing an Instant Win Game or withdrawing funds) before trying again. If you still require help, you can contact us on 0333 234 44 33.
Alternatively, if you have checked the above suggestions and you are still unable to complete the action, it may be any of the following reasons unrelated to your National Lottery account:
Some new debit cards come with a gambling block set as default; please check with your bank to see if this has been applied to your debit card
The card you wish to add is a credit card
The card you wish to add is a business credit or debit card
The debit card you wish to add is being used on another person’s account
Suggestion: Please try a different personal debit card or contact your bank directly to resolve the issue.