No current in this circuit?
"If the points 1,4 and 2,5 are equi-potent how can current flow through the horizontal circuit."


No current flows "through the circuit", current flows through parts of that circuit.


"The potential difference across each branch of a parallel circuit is same and in this case it is 0 and hence no current can flow through the circuit."


The circuit as shown is not fully parallel, only partially.

Did you try to rearrange the circuit to make the parallel parts stand out? If you do it will become much easier to understand.