brown is another 'neutral' color that works with black and white scheme. Would be helpful if you can provide photos or links to the samples you have chosen.

Thank you everyone for your ideas. We are about to paint the walls an off white - double merino, and thought we might paint the doors and pelmets the same and now after reading your comments I think we will leave the timber beams and paint the ceiling between them the same as the walls, and will consider the bar supports too. What do people think about painting ceilings, doors and walls the same colour?

These chairs are easy to recover and the range of fabric available today gives you plenty of choice. I say go for it. If you don't feel up to it yourself get an upholsterer, but plenty of YouTube tutorials about.

Something to take into cosideration would be the amount of light you have coming into the bathroom. Obviously if you have considerable light and air the tile shade wouldn't be too much of an issue. On the other hand if the room is small and not very light filled, then the lighter shades would be preferable giving the illusion of making the room appear bigger and lighter.