The Bren was not the only gun to have the magazine on top, though it's certainly the most recognizable due to how prominent it is. The Soviet Degtyaryov is another example.
I believe the primary reason was so that the gun could be fired in the prone position easier. Afterall, you don't want this to be restricted by the magazine hitting the ground. Firing prone is incredibly important even today as it improves accuracy while making the shooter a smaller target. With the magazine on-top, soldiers could use the weapon in this fashion even on uneven ground.
Another use was that gravity would be able to aid in feeding the bullets into the gun. This helped make the Bren an incredibly reliable weapon, that would only jam after very long periods of use. The spent cartridges were also ejected downward, making firing from a concealed location more effective as the enemy wouldn't be able to determine the location of the Bren by spotting cartridges being ejected.
The drawback to having the magazine on top is that it makes the weapon more difficult to aim. For this reason, the majority of machine gun designs would have the magazine, belt, or drum enter through the side of the weapon. This allowed the weapon to be easily fired prone, while having the accuracy of traditional gun sights (the Bren's were on the side).
However despite the Bren's awkward iron sights, it was incredibly accurate. In fact, soldiers often complained that it was too accurate and wanted a wider cone of fire for greater suppression.
While not directly addressing your question, you may be interested in the replies to an earlier question about the placement of magazines on sub-machine guns.