The stage version of Singin’ in the Rain actually originated in London in 1984 – and as whimsy would have it, I saw this original production then on a trip visiting a couple of friends. That starred Tommy Steele, who also directed. I believe it played at the London Palladium and was extremely enjoyable. And as you can imagine, the question I suspect everyone in the theater had was "How in the world would that they that number?" The answer is that as the scene starts, they wheel out a sort of platform that has raised edges, so when it rains it acts as a sort of large "tub" and catches the water. And then when done it is wheeled away.
(On side note, what was also fun for me personally is that in the role of 'Cosmo' -- played by Donald O'Connor in the original film -- the actor was Roy Castle, who had played the valet 'Sam Weller' opposite my fave Harry Secombe in the Broadway production of the oft-mentioned here musical, Pickwick.)
I’ve posted a couple of songs here from the cast album in the past, but unfortunately there are no good videos of the production. (There’s one, recreated for a variety TV show, but it’s oddly a Gershwin song, “Fascinating Rhythm,” that they interpolated into the score for some reason, so I've never cared to post it.)
At one point, YouTube did, in fact, have a video of Tommy Steele doing the title number, done at the time of the original show – it was for a TV show where people would write in about things they want to do, and this was a little 7-year-old girl who wanted to do the number with Steele. It was absolutely charming -- but alas, about 3-4 years ago the long-time host of the show got charged with some despicable past-crimes, and it was a huge scandal in England. Snce I can no longer find that video, it appears likely the show clearly pulled all video from YouTube.
You can find the two Australian videos on Mark's site with the title song here and "Good Morning" here. I'll be honest, though they're fun to see and I'm glad they exist, I'm bit bit underwhelmed by them, especially the big title number. It's supposed to be a Big Hollywood Movie Star exuberantly exploding with every possible ounce of joy in expressing his new-found love, and to me there's absolutely no charisma and comes across like a matter-of-fact rehearsal just trying to get the steps right. The "Good Morning" video is much more enjoyable, although a little by-the-numbers for my taste and (mostly) I think poorly cast, which distracts too much for me. (The two men who have completely different personalities seem interchangeable, and the woman, who is supposed to be a young ingenue struggling to break in, that's the whole point, comes across as a contemporary of them).
However here's another video of the title number though, from a fairly recent British revival. It's not great either, but fun significantly better stage, and exceedingly more lively.
What seems reinforced to me by all these videos, I think it's a role that is greatly aided by someone with major star power, like Gene Kelly, who has the charisma (and talent) to help make the number burst out. And in the world of London theater and British pop culture, Tommy Steele was at least in that ballpark.
This below is only audio, but here he is from the original London production.