Just to add to my previous post...
To get iTunes to factory reset my phone (this still wasn't enough... I had to then reset phone from device settings after that in order to finally sign back in to my Apple account) was a bit of a headache...
I kept being prompted by iTunes to turn off "Find My" which I could not do as this also required signing in to my Apple account on the device.
I then put my phone in recovery mode (as stated in Mythery's post) and attempted the restore and update options in iTunes. The iOS software began downloading but if it's not downloaded within 15 minutes (it didn't on my connection), the phone will automatically restart.
I found on Apple's site that "If the download takes more than 15 minutes and your device exits the Connect to computer screen, let the download finish" but the download then appeared to go way past it's file size. It kept downloading. I discovered someone else had raised this issue on reddit and it's possibly another bug.
I had to download the software manually via ipsw.me , put phone back in recovery mode, reconnect it to iTunes, cancel the restore and update options that appeared, then shift-click on the "restore" button from the phone's page in iTunes, select the ipsw file, and then iTunes finally factory reset my device.
Again, I was still unable to sign in after all this but realised thanks to Mythery that I could then proceed to erase again, this time from the device settings, and then I was able to sign in again.