Knocking through the old bed recess and living room cupboard to make an internal kitchen is very common in tenements, so it should be possible without any problems from building control. A structural engineer will be able to advise you (without a fee) but will likely need to see the flat before giving any concrete advice. Looking at the drawing I would guess 3x steel lintols, assuming the smaller cupboards are supporting walls. (likely - all original tenement walls are supporting to one degree or another). You would probably need to drop the ceiling in the proposed kitchen/living? room to hide the lintols but that is not a major job.
Guestimate costs:
Fees £1000
Building work £2500 (knocking down walls and installing lintols, maybe a stud wall or 2)
+
Plumbing
Electrics
Kitchen
etc.
You can easy spend £10,000+ doing this kind of thing well (unless you DIY a large part of it, in which case, will it be done well?)
it's not clear what your proposed layout would be, presumably your blue 'paper' wall is proposed by you, not existing or you wouldn't be able to access the space? Would the kitchen be in the corner of the room or completely separate with access from the hall (i only ask because personally i'm not a fan of a small internal kitchen - no daylight etc, and ventilation considerations...)
Another thing to consider - 1st and 2nd floor flats are more hassle for this sort of thing because you can't get into the loft or sub-floor (below joist level) to run services etc. You would have to consider how to get the waste pipe out, which i would guess currently goes near a window on the 11' wall