Just do a sim swap, here's how -
1) You will need to order a new sim from https://giffgaff.com/orders/free-sim
or use one you have lying around the house. Make sure it isn't activated.
2) Logout of your giffgaff account, and click activate SIM on the homepage.
3) Here is where you will enter the Activation code of the NEW sim you're swapping to.
4) It will then ask you if you're already have a GiffGaff account or not. Obviously, you choose yes.
5) This is where SIM swap starts. It will confirm that you want to swap sims. (You need to double check the serial numbers, just in case.)
6) After choosing yes a few times, your old sim should deactivate, and you will lose signal on your old sim.
7) Put the new SIM into your phone, and it can take up to 10 minutes (maybe a bit longer) for the sim to become active. (Personally I would leave the phone turned off with the new sim in for 10 minutes, then keep turning it on and off until you get signal)
8) You have completed SIM Swap! Enjoy.