If I'm correct on the building regulations, you can't go straight from the kitchen/living room into the toilet/bathroom; you need to have a small area that seperates them, which is called a lobby. If you put a door at the end of the corridor where it widens, then this would seperate the two areas. There's a small cupboard there, and then an empty space next to it. As you have no storage space in the flat, I'd make a cupboard to go the whole width.
The middle wall would get taken out (so you'll need to replace the carpet), but I don't think I'd go for a kitchen in the middle. If you took a wall from the doorway across to the chimney breast, you'd need about 5ft for a galley kitchen, and another 6" for the wall, and with about 10ft for the bedroom, you've then you're left with 9"6" for the living room. Now you might get away with 4ft6" for the kitchen, which give a 10ft living room, but that makes it a bit pokey. Putting up half a wall (or 2/3rds) between the living room and the kitchen might be a bit of a compromise, close off the cooker and sink, and make the living room feel a bit larger though. The other problem about having a kitchen in the middle of the house, is that you'll have the kitchen waste pipe running along the side wall of the living room, and you'll need to vent the kitchen, so youd have a square pipe at ceiling level as well - and that's assuming that you can cut through the chimney breasts.
Do you have the courage to knock on the the flats above and below it to talk about the chimney breasts, and see if the downstairs one is using it, or if the upstairs flat wanto to get rid of theirs - it's easy to do, and you'd need to do it under a bulding control notice (£144), but taking them out isn't difficult; it's labout to knocke them down, a pair of gallows brackets to hold the top part up, and then plaster the walls, and put the skirting boards back, then decorate the walls.
How much will the value of the flat increase being taken from a studio, to a 1 bed - hence you don't want to let on what you are going to do