You have to make sure that you fill out the transfer form in the account first. Refer to the steps above in requesting a number transfer.
Contact the EE provider and request a PAC because you want to move your existing number from another network.
Use your EE sim on the scheduled relocation date. Expect that there will be no service signal from both of the SIM (your old and new). Wait until 9 PM to check if the process is successful. See Step 4 on monitoring the progress.
How to Move From Three to Giffgaff
This mobile provider is never limited in changing mobile number even from the Three network.