Possibly a combination of things such as the Rocutaine (devastating drug, I took Accutaine and blame that on my gluten intolerance) plus a lack of vitamin D from the sun.
Vitamin D works in concert with many things and when our D levels drop in the winter, lots of things can go out of whack.
You might look into calendula salve for your lips. I had angular chelitis briefly until I began to put that on the corners of my mouth and it went away in a couple of days and hasn't returned.
Also, I have no idea if it would help, but Dr. Christopher's bone and tissue massage oil has been a miracle for many things.
I also love Traumeel which is arnica cream. Don't know if I'd put it on my lips though.
Hope some of these help, but really, first thing is to optimize your D levels either by taking D3 in large doses, buying a vitamin D lamp, or sitting in the sun at the right time of year and day. I'm not sure what that is for England. For Canada, it's May - Sept from 10am - 2pm.