It shouldn't cause a problem removing the USB cable, it should pick the antenna up again when its plugged in next time. My question would be why is it interfering in the first place? What is the Freeview, Is it a card or a standalone unit? Can you give the make of the Freeview unit?
It sounds like the USB cable is radiating some electronic crap which is being picked up by the mouse/keyboard. If set-up isn't CE compliant this might be the problem.