Rims seem to keep getting wider – the on-trend bikes seem to have 25+mm inner rims. Mud-specific tyres are pretty narrow.

Are there wider tyres now that work in UK winter slop or is narrow still best?

Do people run two sets of wheels/tyres, wide for summer, narrow for winter?

pure mud (rather than mixed conditions) a narrow mud tyre will work best.
1.8-2.2 mud tyres fit i25mm rims fine.
If you’re going properly narrow ie CX type width mud specific tyres you’d be better off with narrower rims. most
You don’t need to crazy narrow I’ve run 1.35 CX mud tyres on a i21mm rim with no problems

New Specialized Hillbilly Grid 2.6 is more like a 2.45 and brilliant on a wide rim 👍👍

Panaracer trailrakers seemed real good on my 26er

Shorty 2.3/2.5. Job jobbed

Depends on your mud. If you want to ride round a muddy field then narrow is still king. If you want to throw yourself off a muddy precipice then bigger and knobblier is better. Something like a 2.3 shorty can give a pretty good balance without being too mad.

projekt baron is my tyre of choice