In some cases the APN can’t be changed when a 4G link is in use. This can also be the case when mobile data is not actually active. To see whether this is what is happening, this might be worth a shot:
Disable mobile data
Set the preferred network type for the GiffGaff SIM to 2G
Edit the existing APN or create a new APN with the desired settings and activate it.
Set the preferred network type for the GiffGaff SIM to 4G
Enable mobile data
Edit: Working settings for GiffGaff have been reported here: