Much prefer the radio to TV.
I listen to BBC Radio 4 (speech based) when it starts up at 0530 and if other things didn't get in the way, I'd listen to it all day, Woman's Hour excepted.
During my insomniac hours it transmits the BBC World Service which provides a wide range of programming.
If nothing appeals there, it's over to BBC Five Live which transmits the appropriately named 'Up All Night'. Rhod Sharp, who runs the programme several nights a week actually does it from his home in Marblehead, Massachusetts. I suppose that if you are going to speak to the UK between 0100 and 0500 then the East coast of the US is the place to do it from.
The BBC, live from Marblehead.
Occasionally listen to NPR/WBUR and 6PR (Perth, W. Oz) online.
I draw the line at the 'pop and prattle' commercial stations. Yes, it's my age...