TS - me or the other driver

I got into an argument with a bloke the other day while driving (in the UK). At a crossroads he was coming towards me to turn right and I was coming towards him to turn right the opposite way. I've always learned that you should pass each other on the driver's side and wait to turn; that way, you have a clear view of oncoming traffic. He came across me on the passenger side and I had to wait and hope. I thought about this afterwards and wondered if he had a point, since convention tends increasingly towards doing what he did and away from what I'd learned. Play by the house rules. [For the record, the argument amounted to little more than a few irritable gestures.]