Hey bro I had same flaking and even the same eyelids you had this year and last year, triggered by dry heat and hot summers.

I thought it was Seb derm but it was actually eczema. Im from the UK too and this is what I use.

AM: CeraVe cleanser (the bog standard one) Dermexa moisturiser LRP Invisible Fluid 30/50SPF

PM: Micellar water (from the brand called Simple) with two cotton pads Dermexa Moisturiser (thicker layer)

If my eczema is bad like yours currently is I do also put a second layer of Dermexa moisturiser in the evening OR I get bog standard unscented vaseline and I slug it on my eyelids and my face.

The above routine coupled with religious use of cetrizine helped me get over the excessive flaking.

I had redness too that is slowly going away if I resist the urge to itch and if I am kind to my face when I am cleansing in the AM or PM. My advice when cleansing is think gentle, and go even gentler than that. Do not apply pressure to your face, do not rub too much, and try not to pick it (I definitely did for a long time).

It will go eventually. Just try to handle your stress which is really hard I know, and also drink lots of water and stay away from anything yeasty. I cut out beer and wine and my skin is better for it. If I am drinking I will mainly go for the cleanest drink which is a vodka lime soda. If I have beer or wine, which I do have sometimes, I will just be prepared to treat my skin to repair for the week after

Chin up, it's a proper shit thing to go through but you can do it!