TOM Daley is a brave guy. There’s the diving, of course. Heights, complex routines, high risk of injury – the stuff of nightmares for most of us. Maybe it was that same daredevil streak in him that said yes to live presenting The One Show recently. The response on Twitter, it’s fair to say, was lukewarm.

The Olympic gold medallist is on more familiar ground talking to fellow athletes in the documentary, Tom Daley: Illegal to be Me (BBC1, Tuesday, 9pm).

The hour-long film opens with footage of London 2012. Out of nearly 11,000 athletes, Daley tells us, only 23 were openly LGBT. “There were more athletes called James than people who were out,” he says. Among those who were not out was Daley.

The hook for the film, and the inspiration for the title, is the Commonwealth Games in Birmingham, which come to a close next week. Daley has done his sums on that too. Among the 56 nations in the Commonwealth, more than half have laws making it illegal to be gay. In Pakistan, Nigeria, and Brunei, the death penalty applies. “I want to find out where all that hatred came from,” he says. It’s a huge task, perhaps too much for one film, but Daley should be commended for trying.

He flies to Pakistan and Jamaica to speak to LGBT athletes, most of whom need their identities to be hidden. There is a common thread running through the interviews: fear of exposure and violence. Videos of some attacks have been posted on the web and Daley watches, appalled. No wonder one interviewee is so afraid of reprisals he writes Daley a letter.

Daley feels the Commonwealth Games should be doing more to make clear that it is an inclusive event where all are welcome. He wants the organisers to explicitly state, for instance, that no country with anti-gay laws will be allowed to host a games. Moreover, and just as importantly, he wants to see a Pride flag in the opening ceremony.

The film is at its strongest when Daley speaks about his struggle to accept his sexuality and come out. Now happily married with a baby son, Daley has not had it easy, with his schooldays a particular trial.

By the by, he is very good on camera, relaxed and fluent, and gets a lot from his interviewees. The One Show’s ordeal by live telly might have been a reach too far for now, but such is his dedication I would not bet against Daley coming back for another go soon.

It’s that time of year again, when Edinburgh rents out its flat to the world and escapes to the seaside, leaving the rest of us to deal with the festival and its accompanying hordes. We really should not moan. Most countries would bite your hand off to have the biggest arts festival in the world rock up each year.

It’s all part of a love-hate relationship some Scots have with the Fringe. While some familiar criticisms find their way in to The Fringe, Fame and Me (BBC Scotland, Monday, 10pm; BBC2 Wednesday, 9pm), this is for the most part a love letter to Edinburgh from some of the biggest names in entertainment.

They’re all here, including Phoebe Waller-Bridge who recalls how she finished writing Fleabag on the train up to Edinburgh The rest was awards-garlanded history and a job writing for Bond.

That’s the Edinburgh dream; some unknown rocks up, does their thing, becomes a word of mouth hit then returns to London ready to take on the world (or at least a spot on a panel show). As most of those here will testify, don’t believe the hype. Eddie Izzard was only an overnight success at the Fringe if a night is ten years. He failed, failed, and failed some more before finally hitting on the right act. While he can see the funny side now, he admits Edinburgh can be “brutal”.

Like many of the talking heads, Izzard is filmed back in the capital pounding the mean streets again. Also returning is Alexei Sayle, who claims to have brought stand-up to the Fringe at the beginning of the 1980s. Memory lane takes him out of town to a field and the caravan where he stayed. It’s still there.

One of the things that dismayed Sayle, and still does, is the class divide at the Fringe. Frankie Boyle agrees. He thought it was going to be very middle class, but it was more than that. It can take serious money to put a show on, placing it out of reach to many. Others complain rightly that there are not enough black artists and women, and in general there is a white, male, laddish, north London feel to the festival.

For all that, it only takes one dream come true story to erase any misery and keep the performers and audiences coming back. Bill Bailey recalls arriving in Edinburgh at 6am on a sunny day, the city glistening and, miracle of miracles, a pub open. It was like Narnia, he says.