A small double bed in a room which is 2m wide? The room is made as a study/young childs room so I can't see it working, unless you moved the radiator.

Why not put in a sofa bed, assuming its for just the occasional use?

If you really want a small double in there: it needs careful measuring, but this one might fit https://www.made.com/meiko-double-bed-with-drawer-storage-pine

Wardrobe on the left hand long wall, then the bed horizontally under the window, from wall to wall, leaving space for the radiator. Maybe make a radiator cover that goes from wall to wall, with a grid above the radiator, but closed on both sides, so it gives space to put a bedside lamp and a book on).

Cabinets above the bed provide extra storage. As do drawers under the bed.

Sorry, didn't draw it properly, I'd let the wardrobe run all the way to the bed.

I think Carolina's suggestion is your best option.

Carolina I never considered this. Thanks

If you are having it custom built, why not consider a murphy bed with built in wardrobes. It tucks away when not in use.

Some turn into sofas when they are tucked away and others into desks so it can be used as a home office:

Also found this image, which illustrates almost perfectly what I meant...

I'm sorry, I'm not in the UK, so don't know where you could source the parts. But in the Netherlands, where I am, you can find everything you need, including made to measure sliding doors, in just about every large DIY store.

You would be better off getting a joiner to make up this as a bespoke item if you want it to fit exactly into your room dimensions. Otherwise you could try Ikea or B&Q for parts but you will have to use filler pieces to tailor it to your room.

I wouldn't cram a double bed into a room this size unless completely necessary? If it is a spare room, I'd opt for a sofa bed instead that can be double as needed? You can get really lovely sofa beds nowadays. If you do need a double bed in there, I recommend as mentioned above, getting a decent joiner in for the job.

I would like a sofa bed as that seems sensible but I am worried about my elderly parents being uncomfortable and I don't have much of a budget.

Actually, I don't see the point of a sofa bed instead of a small double? If you fold a sofa bed out, it takes up as much space as the bed would. And it's not as if it gives you more space for closets? As a sofa it needs space too. Same goes for a murphy bed. Unless you want more space in the room for your daily ballet routines, I don't think it doesn't make much difference if you have a bed or something that folds out into a bed.

Does it?

A well-designed sofa bed will not compromise on comfort. I would definitely check the height if you do go for one just to ensure it is okay for your parents. Alot of companies will also let them test it out for comfort before you purchase.

We specify ligne roset sofa beds quite regularly for clients who want multiple uses out of their spare rooms. In your case it really depends how often the room is used. If your parents are sleeping there daily (or even weekly) a double bed would be preferable.

And as Carolina has mentioned the opened dims of the sofa bed would take up as much floorspace as a double, but I'm sure you are aware of that, as that is the point in them :)

But by using one the room could have more than one purpose. It could be used as a reading nook for example, but multiple other uses throughout the day (even ballet...).

Wow those sofa beds are so expensive. I am on a tight budget.

Check out Ikea for wardrobes. Their Pax are very good. They also have great wall cabinets. Even kitchen cabinets could work for above the bed.