If you have been reading, hopefully you are aware of how important it is to find a responsible breeder. Please start with the Basenji Club of Great Britain breeder list. Puppies predominantly are born fall through winter, and many already have a list for every puppy.. so you may find you need to wait a year longer if you are set on a puppy. However, things happen, homes don't work out, puppies kept for showing turn out to not be right in the ring. So contact them.
http://basenjiclubofgb.org/breeders.php
Northern Basenji Society
http://www.northernbasenji.org.uk/breeders-directory
There is even a link for The Kennel Club for finding a puppy. I clicked a couple... none now, but again, not the normal season
https://www.thekennelclub.org.uk/services/public/findapuppy/Default.aspx?id=Basenji
Finally, if you are not stuck on a puppy, some breeders may have older dogs needing placement... from a year or 2 or older. Also there is a UK rescue:
http://www.thekennelclub.org.uk/services/public/findarescue/display.aspx?breed=1002&id=1823