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Agree on bi-fold doors, not getting wobbly one is doable but expensive.
You could go with a sliding or pocket door?
Make sure you get a quiet washing machine anyway. What will this be above, your kitchen? Maybe think about putting some soundproofing on the floor, it's much cheaper, easier and more effective to put it down then put a floor on top than to do it from underneath and even quiet machines have to spin...
I think the fact bi fold doors always end up wobbly means I'm going for cabinets.
I like the idea of a bit of an open space rather than creating a narrow corridor (although maybe that could be nice too?) but the main issue is there is no natural light so it would just be a large cupboard rather than a real room.