I just bought a flat and when I turn the hot water tap

Right so your not getting any water (even cold) out of the hot water tap?

If the above is true then it suggests the cold water inlet valve to the tank is closed so no water getting into the tank. Some tanks also have a hot water out valve so locate the tank and check the valves for the inlet and outlet pipes are open

Can you take a few pictures from say 1-2 m away and attach them here using the attach\paperclip icon?

Thats not the hot water cylinder thats a pressure vessel design to maintain you central heating pressure as the water gets hot and cold.

Looks like some old fashioned DIY bodged pipe work, from what I can make out there is a circulation pump for your central heat (red pump at the back), and a hot water pump (white pump on floor).

The valve should be on a 22mm pipe so double the size of the small 15mm pipes, typically the hot water feed comes off the top of the tank, which I think is the pipe at the forefront on the left hand side, which goes to a red valve, check that red valve is open (turn anti clockwise, may be stiff so turn in both directions to free it then fully open and leave half a turn closed once fully open.

Its a bloody mess to be frank, I would look to try and work out what pipes go where for example run the hot tap in one room and feel the pipe get hot so you know what pipes serve where so if you can label them, as imagine you will have plumbing issues in the future and a plumber will spend an hour just getting their head round the logic in that cupboard.