Schouiffy, there is indeed a Basenji Rescue in the UK - at times there are sevral dogs there but at present there don't appear to be any but you never know! We are very fortunate not to have as many (even proportionately) to the USA.
What a pity it would be so expensive and complicated to take some of the USA Basenjis. There is often a waiting list for rescue Basenjis here so it's often possible to rehome dogs direct from the original home..
Debra - it is unusual for a club officer to have this position but unfortunately the other coordinators resigned and nobody could take on the job. I don't think that there are the dedicated people here that you have in the USA and Canada. I do admire the hard work that is put in to rehome Basenjis there.