Fixed it, thanks to Zuluman!
For anyone else with this issue here's how I solved it:
Installed stock i9300 UK (BTU) 4.3 ROM using ODIN
Flashed TWRP recovery with ODIN
Downloaded Patched_XXUGMK6_kernel.zip and Patched_XXUGMK6_modem.zip:
Installed these via. the TWRP recovery
Wiped data, cache and dalvik cache, rebooted the device and then it should connect
I'm aware there are a TON of threads similar to this out there but I have tried so many 'solutions' and cannot get anywhere.
I am getting the 'Emegency Calls Only' error on my Galaxy S3 i9300 after trying to use custom ROMs and even the stock ROMs. My IMEI and serial number are correct and I have also tried the ARIZA patch but I still receive the same error.
I'd be very grateful if anyone could help and also if any more info. is required, I'll post it.