Driving on the Left

Someone told me that the reason that the British drive on the left side of the road is an old Roman tradition.

In the olden days when Rome ruled in Britian, soldiers on horseback would carry their sword on their right sides. As they passed each other they would draw their swords. In order to not have to strike across one's body, they would pass on the left so their swords would be towards their opponent.

Sounds fishy to me, but I haven't heard any other explanation. So that's the one I'm going with for now.

Dave