To update your billing information, first log into your account at Birchbox.co.uk You will see a link on your Account and Track Box page with the heading "Update your subscription billing information" or "Manage Payment Methods." Click on this link, enter your new information, and make sure to save.
You will then be billed instantly for that months box (if you have not already paid) and the box will go into process to be received in 8 working days. If you have already paid for that months box - the details will save for the next billing date, the 1st, for the following month.
For customer security, please also be sure that your billing address in your account is identical to the one associated with your card.