Would pipe from radiator to bottom of hot water tank be supply or return?
Why has this radiator been attached directly to hot water cylinder


Seems like a bodge to me.

Traditional UK systems have the radiators completely separate from the hot-water (which supplies taps only). The radiator system is usually a closed loop - with some means of topping up the water - either a header tank in the loft (US: attic) or a valve next to a pressure vessel with a pressure gauge.

 Source: Honeywell

The hot water tank usually has four connections, two for supply and return from boiler which connect to an internal helical loop, there is no transfer of water from this loop into the tank, only a transfer of heat.

The tank is supplied with cold water at the bottom (e.g. from a separate header tank) and hot water to taps is drawn out the top.

 Source: Potterton, modified to show pump, three-port zone-valve, vents and cold water to taps


  Will the pipe attached to the bottom of the hot water cylinder be supply or return ?


Generally you remove hot water from the top and supply cold water into the bottom.


  Where logically should other pipe attach.


Your arrangement seems illogical. Probably the top of the cylinder.


  What could stop it from working?



Sediment clogging the supply pipe or radiator
A valve turned off, blocked or broken.
Lockshield valve (that "other" radiator-valve) needs adjusting?
Air in the radiator
Failure of a circulation pump (if present†)
Bad design or design reliant on specific characteristics of removed radiator.
Programmer/timer set to CH on but HW off.
Failure of HW thermostat or set too low for magic radiator to do its thing.
HW thermostat set too high or insufficient call for HW to sustain temperature gradient in tank needed to support magic for radiator? 




† I believe some very old heating systems used natural convection but I've never seen one‡.
‡ I'm not a plumber.