Can you try the following:
On the activation page here: https://giffgaff.com/activate (whilst logged in)
click on link saying: Can't find your activation code? (Its just below the sim card Picture)
The box to enter the activation code will change slightly and will allow you to enter the 13 digit SIM serial number (in some cases this may be 16 or 19 digits), which can be found on your SIM card right before 4Ggg4.
Hopefully that should allow you to swap your sim if not then follow Sloz's advice above
All sorted now guy's, my partner reminded me that we had a new spare sim laying around so I activated that one successfully. I'm all up and running on my new phone! Thanks for everyones help 👍
Sorry for not replying sooner but was having some login issues
Thats great news, Glad your all sorted.