Simply change your number for a new one.
If you have an active giffgaff number, and you want to change it for a new (random) giffgaff number:
(this will replace your current giffgaff number on your existing account with a new number. All credit etc will be preserved). This is a permanent change, you cannot get your old number back if you change your mind.
Method 1 - Self service - only available between 04.30 and 21.30, and can only be used twice per account (minimum 24 hours between changes)
Log in here: https://giffgaff.com/profile/details#msisdn
Read and understand the instructions and warnings
Click 'Change my number'
On the next page confirm that you wish to go ahead.
Your number will be changed within 4 hours.
Method 2 - Ask an agent
Contact an agent, using this form: https://support2.giffgaff.com/app/ask/SIM-and-number/Changing-my-number/form/
When your new number is ready, you will be given instructions on what to do next.
Your number will be changed within 24 hours.
Restart your phone after the 4 or 24 hours indicated above, and every 30 minutes thereafter until you regain service.