Keeping in mind that the TL as written when i ended was going in 1943. The map is from around 1960.
BEtween 1943 and 1960 a lot of things happen.
One of those things is that a lot of the exiled governments and form free-french style colonial states sometime after 1943 as the Nazi policies get out of hand, as they inevitably do.
So it isnt technically UK taking over them. It is states declaring for the "free french" and "free belgium" and so on. After they ATL UK is unable to free most of europe they start negotiations on the peace treaty and it is, in effect, a "as borders stand now"
So, most of Africa due to being strongly free-french-belgium etc due to very little strict axis support end up declaring for UK instead, once the first real news of the worst Axis things in ATL (they will be there just as in OTL) a lot of those countries and their colonies that still CAN get out, do get out of the Axis.
This is followed in short by a lot of political restructuring but after the Axis effectively lose power to a right wing military rule that slowly turns into a german lead state. But that takes over a decade to tear down most of the Nazi infrastructure. By the 1960's most of Africa is controlled in a "UK-French protectorate" and "UK-Belgian Protectorate".
So, Belgium and most Axis players "lose" africa, simply because all the exiles from Europe slowly migrate closer to their original culture zones and by 1960's the culture in Belgian Congo and Belgium itself is so separate that effectively Belgium loses control.
Think, Commonwealth of nations but much more centralized, so Africa is effectively in its entirety a UK colony, some of the N-Coast is Axis and Ethiopia and such are free.
As the situation in t he 1960's and onward develops, Africa will see its version of cultural revival and independence movements but it will be a much different war than in OTL. It will also lead to a much better African Union by 1980's. Rastafari culture will play a significant role in ATL africa due to Ethiopia being significantly freeer.
EDIT: Good lord, never write with a hangover, the spelling is so atrocious that its unbeliavable. Try to muddle through.