I very much doubt that you will find a Basenji in the UK this coming winter. Covid seems to have convinced so many people they can now have a dog - and they light upon Basenjis for a number of reasons, often without going thoroughly into the challenges of ownership of one of these challenging little animals !
All the breeders I know have full waiting lists even after filtering out all but the most promising future owners. I haven't bred for over 10 years but enquiries for puppies still come in, several a week - two just this morning.
We just have to hope that irresponsible people won't mate un-health-tested dogs, just to cash in on demand.
It all depends on the allergy - whether a Basenji will or won't affect your wife. They shed, often pretty constantly throughout the year instead of one big winter-coat moult although some lines do have that.