Tesco provides ADSL internet (i.e., through your phone line).
So, you want something like this:
http://www.ebuyer.com/product/52244
(I can recommend that site, as well as Netgear as a brand. Linksys are also good.)
You currently probably just have a modem from Tesco, which goes between your phone line and eMac. This box linked above just replaces your old modem box.
If you want your eMac wireless too (I'm assuming your eMac is close enough to the phone line that you can just connect it with a cable to the modem/router linked above), then you need to buy a USB wifi dongle, setting you back about a tenner (ebuyer also stocks them too).
But wired connections are always better than wireless, so since it's a desktop machine, stick to wired if you can help it.