From what I remember of the studio I presume they must be standing!
Yes they're standing, they're seen on camera in virtually every edition of the programme
I can also remember how scratched, buffed and grotty the clear table they have in the middle of the studio looks for real. Tried to take a photo of it, but the grottyness didn't really even show up on that.
That is not unusual to The One Show, TV sets always look a lot shabbier in real life especially those that have had daily use for years