I have a desktop PC which has a be box modem which is plugged into the main BT socket, I am buying a new laptop which I want to use on the second floor where there is no phone line, do I need to replace the be box with a more powerful wi-fi router?
I'm not familiar with the "be box" but a Google search suggests that it is actually an early model of Wireless ADSL Modem/Router, operating more effectively on 802.11b (11Mbps) than 802.11g (54Mbps).
That being the case, it may already do what you require and let you connect "wirelessly" to the internet with a Laptop on the second floor. It's worth giving it a try and, if it doesn't work, then look to replacing it with a new Wireless ADSL Modem/Router.