So....khm, would be the following:

Adding any kind of wall to make separation beetween living part and kitchen will ruin your flat and turn it Peckham residental.
So, your goal to make semi-luxory flat will be dismissed totally.
Fore sprinkler system is not so much expensive, so please go with it. Even, furthermore you have the bath over, in the loft, so it is not hard to provide water.

Small window should be removed, no benefit of it, and it just makes issues for wardrobe closet.

The most intreresting area, overalll!
Small studio room is cutaway to place the entrance closet, facing the hallway.
Left wall, when entering the studio room is also used for hanging the jackets, very useful.
When entering the kitchen/ living room, the part of kitchen is used for entrance shelves and similar, look at the images, please.
Do not be afraid, of placing all that stuff, into kitchen, as it is not kitchen indeed, it is just part of kitchen elements used for shelves.
Furthermore, you can sit on first few steps! Or you can place the chair somewhere near chalk board.
Drawing board is there to make the apartment livingfull, you are passing near board when leaving or entering, so you leave the massage for your family.
Washing units are palced in closet big ones, in kitchen, behind the wooden elements, hiden by the door.
Stairs is very simple to hold the hiden closet, below the stairs, see images, please. That closet should be used for whatever.
Fireplace, should be oil or gas fireplace, no wood, as it would make so dirty the whole apartment!

Very small, and it even smaller after changes. But, you do not need more space than it is, righ now. Entrance clsoet is much more usefull than 35cm of small room.

As it is, nothing more to tell.

Everything is clear, except strange stuff on wheels, I guess.
"Strange stuff on wheels" is moving wardrobe, which is placed in small storage area, near bathroom.
As it is very hard to reach into its deepness, I decided to make this unique wardrobe. With good wheels, even 5-year old kid can move it.
Furthermore, your client will have some unique and very special just for this apartment.

I would go for floor heating system, as it will make the space more clear.
Otherwise, you'll have enough room for placing the radiators below the windows.

I hope you'll enjoy in this design.