There are many ways of connecting two Computers to the broadband connection but your TV is just that - a television receiver. You can also often connect a computer to a TV screen for larger pictures but if you want to surf independently then you need another PC or laptop to share the broadband connection.
However - with advances (every minute it seems) you never know. I might just be be out of date!
No need to spend £500 though - you can pick up a decent used computer for £75 - £100.