Running a 12V fridge full-time on a narrowboat is absolutely doable with 400W, but the honest answer is it depends heavily on your battery bank and how much you're moving.
On my boat I've got 400W of panels (two Renogy 200W mono on the cabin roof) feeding a 200Ah LiFePO4 bank from Fogstar. The fridge — a Waeco CFX35 — draws roughly 2-4A depending on ambient temp and how often you're opening it. In summer that 400W array comfortably covers it plus lighting and phone/laptop charging. In winter it's a different story. You're looking at maybe 3-4 usable peak sun hours even in the south of England, and panel output drops significantly in cold, low-angle light.
Key questions I'd ask:
- What's your battery capacity? With lithium you can actually use most of that capacity as a buffer overnight. On lead-acid you're restricted to 50% DoD, which changes the maths considerably.
- Do you run the engine regularly? An alternator with a decent B2B charger (I use a Victron Orion) gives you a meaningful top-up on cruising days.
- Where are you mooring through winter? Shaded canals under tree cover will murder your harvest.
400W is workable for fridge-only if you're sensible, but I'd honestly say 600W is the comfortable threshold for year-round liveaboard use without anxiety. The roof space on most narrowboats can accommodate it.
What's your current battery bank situation? That'll shape the advice considerably.