There was a notification icon in the address bar which told me I had an update. Update was around 64Mb - over wifi took about 10 minutes to complete
You can also check for updates in "Settings/About/Software Updates"
Yes, I am in the UK and with O2, not T-Mobile here.
We had our HTC One release in the UK on O2 on 5th April, got mine about two weeks after that. If I remember what I have read correctly, the US didn't get the phone release until May, which means you might be behind us by a few weeks for the update.