I can’t help you with UK suppliers but have you tried searching with some combination of the terms LiFePO4, RCR123A and/or 16340?
Sure seems like Liquivision know how to charge for cells…
If looking for rechargeables, be sure to get LiFePO4 cells which are nominally 3.2V (max 3.6V) rather than the more common LiIon 3.6/3.7V (max 4.2V) cells used by the flashlight community.
I am guessing the battery choice settings in the unit are related to the device’s ability to accurately report the battery level as rechargeable cells have a different discharge curve to primaries.
Will I use the dive computer and the transmitter every summer weekend and every day on diving holidays.
I take liveaboard dive trips so rechargeable are essential.
I did try single use batteries when I first got the computer but found them to be unreliable. There are some cheap single use batteries around but they come from China and do not have a good shelf life.
As my dive computer is part of my life support kit I found the K2 LFP 123A to be the most reliable. There seems to be a problem getting them in Great Britan
Having no fins myself, I am not a fan of putting my head under water. So I am the last person you should trust on: LiFePo is LiFePo. IMHO you are not the only person in the UK with this computer. There must be a diving forum or two where this question has been posted on.
There is maybe an alternative LiFePo4 3V Battery, I call him the blue/yellow one, there is no exact labeling on it, but it´s tested from well respected members in the German flashlight scene, from Megalodon here in the MesserForum (Post 3) in comparison to the K2 battery (Post 2)
It seems shipping to England is no problem, depends on the value of the order with Max on 7,95€ with value under 30€ (under ´Versandkosten´)
Maybe that´s an option for you