I just reverse biased the 1n4007 with a 12v dc supply(from a wall adapter) and found that even though its reverse biased it has a voltage of 0.7V at the other end. where as the 1n5819 has a voltage of 2.5v at the other end.
I think you need to elaborate on this statement, because as it stands it does not have any meaning. A voltage is measured between two points. Between which two points are you measuring 0.7 V ? And what does your complete test circuit look like?
In particular, if you apply 12 V DC across a diode in reverse bias, the voltage across the diode will be 12 V. Are you putting a resistor in series with the diode and measuring across the resistor perhaps?
As for your subject question, yes, all diodes have a leakage current. For some diodes, like Schottky diodes, it might be significant.