I paused live TV last night for so long that I didn't want to watch it there and then. It struck me that I ought to be able to do more than simply press stop and discard the programme (I wanted to watch something else) but can't see a way to do that. Am I missing something or can you simply not do that?

In short, no, the software doesn't have that feature. A workaround, albeit kinda defeating the object of the timeshift feature, is to do an instant record instead (press record instead of pause), and then go to the library and select the recording there to watch it while it records.