How can I set a family member to have their own independent account?

Go to My account, section Family members and select the family member in question. Scroll down and you'll find an orange Make independent button. Click that!

However, you'll only be able to do this on two conditions:

1. The family member is 16 or over
2. The family member has a verified eMail address

For the latter, the family member would need to log in themselves and add & verify their own eMail address by going to My account and opening the Emails section.

As a family head, you could do this yourself on their behalf, of course, by navigating to their account from your account drop down menu top right.