Spoke their Tech Support and they said they have been having major issues with ESIM download and I would have to visit a store to get a QR Code Pack - and they booked me an appointment.
A short while later, I was on the EE Website (I had previously been using the EE App to try and download) - and I noticed an option to replace SIM/ESIM on the website.
I clicked the above option and it showed me a QR code to scan + add the ESIM to my phone - which I did. They then sent an SMS to authenticate and the ESIM was activated - and I was able to remove the physical SIM from the phone.
