Hmm. It would seem that a real advantage to a desktop PC is the ease of configuring a directional WiFi receiver antenna. I got one for my parents about two months ago (http://www.signalking.net/en/product...p?tid=6&id=122
), and it's working great -- despite the strange-sounding advertising text in my link.
First make sure that you are using a different WiFi channel than your neighbors. I'm guessing that there is some utility built into the tablet that would allow checking competing signals, and a utility built into the router that lets you change the channel.
If that doesn't work, I'm thinking you can't do anything more on the receiver side, since it is built into the tablet, and so need to boost the transmitter signal. This will likely be more expensive than a receiver-side solution. Here is a product that I haven't tried and that may or may not be marketed in the UK:
P.S. It may also be possible to buy a cheap (Tenda brand is cheapest here and seems OK) router and configure as a repeater. Here is a LifeHacker page I can't vouch for: