Alex Gabriel at FreethoughtBlogs:

Here is the clip that spurred reports. The entire exchange occurs within the first five seconds.

‘Let’s get right to the crunch here,’ says host Keith Lemon – persona of Leigh Francis, one more straight comic in the David Walliams mould who thinks ‘act queer’ is the fastest route to funny. ‘You’re a gay man now.’ (This is, as has thus far been largely overlooked, a reference to a popular Catherine Tate sketch.)
‘I, ah…’ Daley replies, sounding a bit uncomfortable. That’s it.

Admittedly, his diction isn’t clear. A proper journalist’s transcription, and well-known journalists have hired me to give them, would render it simply as ‘[indistinct]’: the second word could equally be ‘agh’, ‘ugh’, ‘yeah’, ‘know’ or something else. Outlets desperate for a bi-now-gay-later scoop seem to have rounded it up to ‘am’—then delved into wild, opportunistic paraphrase of what they hoped he’d said.
Even if Daley had answered ‘I am’, low-brow comedy quiz programmes on ITV aren’t quite the forum for Q&A on nuanced identities. Plenty who sail like me in vaguely bisexual waters would, I think, have shrugged along rather than correct Francis.

Sounded like an "I am" to me. But, no, Tom Daley didn't use the word "gay" in that brief interview.

But after the host described Daley as gay—which he did twice—the British diver went on to say this about why he came out about being in a relationship with a man on YouTube: "I wanted to be able to say what I wanted to say on my own terms without anyone twisting it." If the host of the show was "twisting it," i.e. suggesting that Daley was something he was not, you would think Daley would've corrected him. But Daley didn't. That said, Daley is young, the exchange was rushed, and the format didn't exactly allow a nuanced convo about sexual identity. So Alex may have a point.