Actually looking again it looks doable.
The kitchen diner is fairly large, so no dining table needed in living room. I would put a smaller table in kitchen so it’s not so cramped though
Child in bedroom with bath. Ours is 3 with en-suite and he’s never played around in it. Means you can shower early or late downstairs without disturbing sleeping child.
Add half wall and then glass framed top half at side of stairs. Will made it more private and separate from living room, plus help with noise from downstairs up.
Add built in narrow bookcases either side wall where old downstairs wall division used to be. Then you make that one room semi open plan rather than full, and can have tv and sofa area at back, and armchair, play area, study at the front
Add front porch. Gives somewhere for shoes and means you don’t open door straight onto living room. Look at others locally for ideas
The garage gives option of converting later to proper office, and storage area if needed.
If this is bottom of budget, then you have £ left to make alterations