Mechagodzilla I saw for the first time when I imported Sony's 2004 DVD. Despite it getting a video release over here I don't think it ever actually aired on TV, or if it did it certainly wasn't as common as the others and I never saw it. I wouldn't be surprised if GtTHM was the third of those other films that got video releases since there are only a few it could have been, but I never saw that air on UK TV either, nor GRA. The first time I saw those two was when I imported the Classic Media Godzilla DVD box set.
I remember not being too taken with GtTHM the first time I finally saw it, but it was cool seeing the origins of so much of the stock footage of Ghidorah's (and other monsters) destruction from later movies, and it's one I warmed up to more when watching it again years later. GRA I've always felt was a little underrated. Certainly not to some sort of "it's secretly one of the best of the series" levels or anything, but it has a cool atmosphere I've always kinda liked.
It seemed like pretty much once the 2000's rolled in, Godzilla movies just disappeared over here, both on TV and on DVD. I can't even honestly remember the last time I saw one on telly, or saw a listing for one that wasn't Shin or one of the American ones. All you could really get on DVD were the US cuts of King Kong vs Godzilla and King Kong Escapes, eventually the original '54 film, then the Monsterverse movies once those started coming out. We did get Shin Godzilla not *terribly* long after other territories, and that's shown on TV. But before the Criterion set was released over here pretty much the entirety of the Showa era films were unavailable for about 20 or so years. And there's still never been any UK releases for the Millennium series or half the Heisei series, as far as I'm aware.