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Doesn't clicking the power button on the top of the phone turn the display off and lock the keys for you?
You could try displaying the night mode dimmed clock and see if the internet radio will still work with that. Click on the HTC clock then press the little moon and star icon (it's towards the bottom of the screen).
Use myPlayer to stream BBC radio. It continues to stream in the background, even with the screen off.
myPlayer v0.84b Application for Android | Multimedia
I'm after some kind of app which allows me to turn the display off.
I want this because if I'm listening to internet radio via the BBC iPlayer, the display remains on which seems a waste of battery. Also, it would prevent accidental clicking of web links.
Use myPlayer to stream BBC radio. It continues to stream in the background, even with the screen off.
myPlayer v0.84b Application for Android | Multimedia
There are night clocks on the market although I haven't tried them. This one for instance Night Clock - Android app on AppBrainUnfortunately I'm running stock Android Froyo so I haven't got the HTC clock at the moment, but it's a useful suggestion, thanks.
Will copas2's Proximity Tool be any use in your situation:
http://androidforums.com/htc-desire/94942-use-proximity-sensor-disable-screen-while-pocket.html