If you no longer want to use giffgaff then you simply stop using your account. You can't close it entirely bit you can remove all of your personal details and stop any recurring payments that you might have setup.
If you have a recurring goodybag and want to cancel it
Log into "My giffgaff" https://giffgaff.com/dashboard
Directly underneath your community membername you will see your current and recurring goodybags.
To change your recurring goodybag go to the "My payment details" page https://giffgaff.com/profile/payment-details
Locate the "Recur your goodybag" section at the bottom and click on "Change" to display your current recurrence settings.
Untick the Recur your selected goodybag box and click on Save recurring settings
Go back to "My giffgaff" https://giffgaff.com/dashboard
and you'll see that your recurring goodybag has been replaced by the following message " You can switch your goodybag to automatically recur every month".
That's it, your recurring goodybag has been canceled. You'll be able to select a new recurring goodybag by clicking on the "recur" link.https://giffgaff.com/profile/payment-details#goodybagsettings