Thank you for the link to a wikipedia disambiguation page. I remain none the wiser.
Third possibility down
Tig, another name for tag (game)
Well spotted, there is indeed a direct connection between an Alan Partridge sports commentary and my username. Other options considered were…
Epileptic fridge boy
Smalltown gypsy massacre
Immaculate pasta
Astonishing bomb queen
Christ’s chin
Armando Iannucci is a comedy hero of mine.
Sinéad O’Connor
Back in the early 60s in my somewhat oldfashioned grammar school. Baron Greenback’s game was known as British Bulldog, and was reserved for the last PE lesson of each term.
Country dancing was taught in my primary school, which was mixed. I’m not sure if they deservd a medal for courage or a Darwin award for encouraging a class of 30+ 8-year olds the rudiments of Gathering Peascods, let alone Strip The Willow. But then, that wasn’t that many years after this famously innocent radio programme for primary school Music and Movement classes
At my single-sex grammar school there had been attempts to teach ballroom dancing in common with a local girls’ school, but by my time, they had realised that was somewhat vieux chapeau, what with these Beatle chappies and all that sort of thing.
At my school British Bulldog was purely a kid-organised playground thing. It was quite a robust game as I recall, and the teachers or the janny would stop it once they noticed a game had started.
There was another chase game called Kiss, Cuddle or Torture that the girls took the lead in. The Torture choice when caught was either a Kiss plus a Cuddle or (what we called back then) a Chinese Wrist Burn. Interesting dynamics in that game.
Doing PE in underwear in Britain?
You’re not allowed to, and if you ask why I’ll tell you why I’m not allowed in Westminster Abbey anymore.
So this is how all that buggery gets started
We played British Bulldog in which one or two players would line up against everyone else. All the others would “charge” (we called the game British Bulldog Charge") and aim to get past the stoppers to the other end of the playing area. Anyone that the stoppers stopped became a stopper for the next charge. Repeat until only one player has not been stopped and that is the winner. It was a very rough game and surprising that we played it at Cub Scout meetings. I cannot see that happening these days.
I loved British Bulldog and it was the only game I ever enjoyed.
We both were: I didn’t know that tig was a synonym of tag and thought it was a typo for tag. So I was referencing Tigger from Winnie the Pooh who, if he played tag/tig in 3 dimensions, would have the handicap of not being able to climb downward.
Baron Greenback, your posts in this thread are enough to make me think we went to the same school.
At my primary school, big navy blue knickers were part of the uniform. PE was done in those plus vest, until primary five or six.
At secondary school, there was a simple system for dealing with forgetting your PE kit. Each time you forgot it, you got a black mark. And it was literally that - a black mark against your name in the register. Once you got three, you got “the belt”. This was the Scottish form of corporal punishment, also called the tawse. Wikipedia Link
My Dad’s job moved us around Scotland a bit, but things weren’t so different at whatever primary school I ended up at. It was navy knickers, horrific y-fronts, Shipwreck, British Bulldog and Kiss, Cuddle or Torture everywhere. 
And Strip the Willow, which - let’s face it - amounts to two falls, a submission or a knockout.
And the Janny that ruled the playground with an iron fist.
That game is what we in the Antipodes called Bullrush, although I was fully aware that other people called it British Bulldog - possibly more of a South Island thing.
Schools here in NZ are reintroducing it as a playground game, although as a “tag” variant and not the “tackle” version I played as a kid.
We played with those in the middle calling names of runners, and if someone got through there would be a bullrush.
One of my fondest schoolday memories was being called to run early in a game of bullrush, dodging the fastest kid in class, getting ankle tapped from behind at full speed, and executing a perfect diving forward roll back on to my feet and crossing the line.
Bullrush 
Yes, we called it both those, and Red Rover, in my tiny South Island locality.
My first thought is that I had crushes on girl as young as age 5 and 6. Playing doctor, which I didn’t do, is something that happens even earlier. So I don’t agree that they are pre-sexual.
My second is that they’d still be wearing their underwear. Is the idea that they then take them off and wear the rest of their clothes? Otherwise, the same problems would apply to the clothes as to underwear.
Third is simply that I was pretty active as a kid, yet I never got noticeably wet from sweat. And I lived in a hotter summer climate than in the UK. Sure, kids sweat, but not like in puberty. And what sweat you do have doesn’t stink nearly as bad–hence why few kids wear deodorant, and often even bathe every other day.
And my final thought is, even if I concede an issue, why not just have some backup clothes the kids can wear? That eliminates problems 1 and 2. Every school I went to had them for dress code violations. Why not for kids who forgot their gym outfits?
But presumably kids don’t wear “burkinis” to go swimming.
I’m not defending PE in underwear policy; clearly it’s had its time, we’re more aware of paedos than we were.
It’s just interesting how the same amount of material is crazy in one context and not in another.
It’s just Red Rover in South Africa - our variant, the first one or two got to nominate a person to run over .“Red Rover, Red Rover, can Bobby come over?” meant Bobby had to try and cross the line, if caught they became a catcher but if they was successful in avoiding the catchers, everyone then charged and the others could try to catch them. Rinse and repeat, last Rover wins.