I don't know if I'm explaining myself right here, but basically,
one half of the gate is locked with a padlock.

I know exactly where you mean because I used to live on the Isle of Dogs and
have cycled through that little park numerous times. Can't help you as to
why the gate is closed, but if I recall correctly then it's not much of a
cycle path anyway - quite narrow and the boundary between the two halves is
not respected by pedestrians, so I would have no qualms about using either
side of the path/gate. In any case, I reckon it's probably nothing more
sinister than that the person whose responsibility it is to open and close
the gate just can't be bothered to do it.

d.