Approximately what sort of timescale are we talking about? e.g. would he have gone in the 1960s, 1980s, or quite recently? You could see if he suddenly disappears off the electoral roll (without an accompanying death).
There might be government organisations who do have details (e.g. if he's claiming pension from abroad), but I doubt they will be willing to hand out information. For that matter, in many cases the government simply doesn't know. You don't get an exit interview at the airport asking how long you're going to be gone, and even if there was you could do what my sister did which is intend to stay for a couple months and end up finding a job and staying more permanently. (There are not actually accurate figures for how many Brits now live abroad).
Depending how common his name is, it might be worth just going through the phone books for the major expat destinations.
Other possibles: if he is still is contact with an alumni organisation or similar, they are usually willing to pass on a message (they don't hand out details but will forward yours to him).
If you know where he was last living, particularly if it was relatively recent, a notice in the local press may turn up a friend or neighbour who can put you in touch or at least knows where he might have gone.
Tracing organisations such as the Salvation Army can help with both those in the UK and abroad, and I'm sure they've dealt with cases like this where someone moved abroad without the family knowing. I would talk to them first (if it's a case where you're trying to reunite with a lost relative you haven't seen in X years - they do not do "genealogy" requests)
