I’ve been away for a few days so only got a chance to have another go last night. My issue was described earlier in this thread and, although related to the same controllers, was different to what Brian has described.
In case it helps others avoid the frustrating journey I experienced, I have resolved this by starting from scratch. That is, I took the SD card that I had originally received as part of the kit and replaced with a new image using the instructions at First Installation - RetroPie Docs. I used the Raspberry Pi Imager, selected the RPI 4/400 image and wrote this to the card. Fortunately I had a USB card reader so this was relatively easy for me to do. After startup, I was able to pair the controllers and they just worked like they should have. I have also since upgraded RetroPie and the OS - the controllers still connect via Bluetooth, no problems. I’ve shutdown, checked the next day and the controllers automatically connect.
I don’t know what went wrong initially in my case but my suspicion is that it may have been when I originally paired then removed a controller pairing. I think some configuration may have not been entirely removed and this blocked re-pairing from working properly. This perhaps left me in a weird state that I could not return to a clean slate nor get it working. Maybe this was the cause or something else - hard to prove. Regardless, only starting from scratch did the trick. Glad it is resolved so I can actually play games rather than learning RPi commands 
