Firstly is the only reason you can't get the BBC channels now is that you can't tune a receiver in? If so then what you could do, assuming you have friends or family in the UK, is get them to tune a receiver box e.g. Humax Freesat box on their dish in the UK and send it to you. I did this for a friend in France and it has worked fine for the past 2 or 3 years, just don't update the location settings.
As for your Tablet question the only way that I know of to do what you want would be an iPad and Apple TV. Not sure that the LAN connection is a gigabit one though.