What can I add to this? Sometimes I wonder whether an event like BBC Young Musician has got the wrong approach, i.e. start 'em really young and push them to an incredible level - full concert performance standard - at a really tender age! Though the results are fantastic, I sometimes worry about this. Not just about the kids themselves, I mean. Any late starters out there might well be put off by this, just assuming up front that they are out of the loop and why bother?
So, about the rest of the early starters - like myself. It's nowhere near like this, of course. I started the piano at about age eight. I began with a flourish, bagging my Grade 1 with distinction within the first year. After that I plodded on with the lessons (getting up to Grade 5 - scraped pass) until I left school, then I dropped them. In the forty years since then, I quite often bash away at the ivories, just for fun, but I have no performance ability and never will have. And my family, who - er - endure all this, know it.
So what about late starters? Perhaps with the right motivation, they can pull something off where I never did? I'd say, if you really want to do it, go for it whatever your age. If your feeling is, instead, you really ought to do it, forget it. Wrong reason and you won't stick.