OK, looks like the WAP thing is the way to go for me. I found this on amazon...
http://www.amazon.co.uk/dp/B002YETVV...SIN=B002YETVVE
...for £18 delivered.
So if I free up ethernet port 1 in the Linksys & plug this in I should be good to go after the setting up kerfuffle.
Thanks very much for the information.