Are you saying you've changed from the white to the black?
Are you saying that you're only bothered about the switch on the left which is used as a 2-way switch?
Final query (from me), are you sure that on the right hand switch that the 2 red wires, which come from outside, haven't been...
This (link):
https://www.electricpoint.com/hager-sollysta-cooker-control-unit-50a-white-wmcc50.html
would use a double backbox but might need a deep one. I'm sure other manufacturers do similar things.
Just a possibility, once upon a time there was just 1 "13A" cable and 1 daisy chain cable but 3 lights, so chop daisy chain cable in 2 and use both ends.
I don't believe that's correct.
If I've understood properly then it should be a case of moving the black wire from L1 to L2. But do be very careful as ETAF recommends.
Obviously I'd defer to the professionals here, but would a flex outlet plate such as:
https://cpc.farnell.com/click/cca017/outlet-plate-20a/dp/PL10173?MER=sy-me-pd-mi-alte
on a 16mm pattress be the slimmest solution?
They're certainly deemed to be big enough around me (near Pimlico tube station), there's one in the lamppost outside and several in the street as a whole. Also I frequently see cars being charged, from a lamppost, in the Chelsea and Battersea areas.
I believe you'd be better off asking this on the Plumbing and Central Heating forum (regrettably you'd probably need to explain, again, how you got to this query).
Apologies, I've been away from t'internet. Yes they were clear that this is irrespective of any other thermostats (room or TRV), I expect you've got this message from the others well before now.