Who is being unreasonable about the heating?

To be honest it sounds as if the issue is that the outside doors are letting all the heat out. There should be a lobby or at least 2 sets of doors to save as much heat as possible, otherwise even if the reception area were heated to 25 degrees, the temperature will still plummet on cold days.
Is there the possibility to put up
A screen around the reception desk to cut some of the draft?

A needs this and will never be cold again.

www.argos.co.uk/product/9190629?clickPR=plp:1:63

Only people who don't feel the cold think you can just add more layers.

What does A wear to work? Are they in a cotton dress and bare legs?

But also sounds like A is being unreasonable to not even turn the radiators down to 0. It shouldn't get that warm surely if the rads are switch to off!

Yes do this. Get the hive thermostatic that can go in individual radiators and zone off each room to its own temp!

Can you not swap seats?

Twelve degrees is far too low and although there isn’t a set law there is guidance for it to be above 16 for office based jobs and 13 for labour intensive jobs. Health and safety states that temperature must be comfortable. I would put in writing my intention to raise a form dispute with ACAS if they refuse to intervene and sort it. They may not want confrontation but as management is their job so sometimes you have to do things in order to get the ball rolling to make sure that they do.

Get an oul filled radiator ti go near your desk. They are a very low fire risk

I was always freezing at work and had a blanket and hot water bottle as well as layers of woollen clothing. As yet another winter dawned I decided I'd had enough and told my manager that I was handing my notice in.
Within a week I had a portable heater. Within a month they'd repositioned the air ceiling vents, eliminating the draughts.

So, A is being unreasonable and you'll have to be even more unreasonable than her in order to get management do anything about it.

The hot one can't do anything to reduce the heat the cold one can add extra layers

I dont know the answer other than 12 degrees is too low.

Tgey do say heat the person not the room so could you get a heated gillet. They have a battery and some charge via a USB. My sons school is outdoors and a lot of staff have them.

I'm not sure what the fire risk of a portable heater was, but they also make infra red things that wall or relining mount.

That sounds very cold for a desk job - if you are not moving it's very chilly at 18 degrees. I would get a temperature logger, share the data and that will make it clear it's not acceptable to have the heating off. There is a minimum legal temperature for workplaces (I think 16) and if it's dropping below it that will be your key point. If it isn't you may have trouble.

Can they add a thermostatic radiator valve to the one in reception so it can be controlled? Can the person who is too hot have the aircon on if the heating is also on?

I'd say turning off the radiators in the clinic is the simplest solution and that A is being unreasonable. If my office was 12 degrees I'd be going home!

I think you should keep a written log of the temperatures during each day. And maybe a log of what you’re having to wear each day too! Then I would escalate it again to management in writing.

Is it even legal in the UK to let someone work a desk job at 12 degrees?

A is totally bonkers, not allowing the heating to just pass through the room.

Does the one who keeps turning it off not have thermostatic radiator valves in their room so they can just turn their radiators off? That would be the best solution.

Plug in seat warmer? Double doors to not let all the cold in? Get the heating changed to a thermostat per room? Reassess the fire safety as a plug in oil heater really is safe? It feels like there is a solution that doesn't involve grown women just stropping and sulking.

B needs to get a hot water bottle to stick the the jumper or rest on the lap.

We'd be having the same argument! My ideal working temperature is 23.

A is being unreasonable. I'm a cold preferer and hate it being too stuffy but A has the option to turn the heaters off. If they are completely off and never come on there's no way they will still be 'a little bit warm' and even if they are it's going to be negligible.

If the reception area only reaches 18.5 even with the heating on all day then the clinic room without any heating on is not going to get much hotter (if it even gets that hot), and that's a completely reasonable temperature to work in. If patients are sitting with their coats on then the reception area can't be that warm.

I appreciate there's a reason you didn't specify but are they noticeably different weights, as that can affect how much you feel the cold but can also be harder to address sensitively.

If patients are complaining and B is unhappy then of course A needs to turn off her radiators and cope - patients cannot wait in 12 degrees

Do patients wait in the reception area that is 12 degrees which is far too cold