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It is, yes, however the room, whilst not exactly narrow, has been reduced in width by a previous taking a slice off it to put storage in the hallway. With a short double bed you will probably just have enough space to walk round the end of the bed and between the existing fireplace (it will look a bit goofy though). Anything longer and it won't work.
Also I think in what was the dining room below we will remove the chimney there too so it will make sense to get rid of this one as well. Will keep the fireplaces in the lounge and the bedroom above it though.
Built-in wall could also go on the other wall, I'd imagine it's easier to relocate a radiator than removing the chimney?