Well, at least British African colonies might actually beg the British to keep them. They don't want to be independent and have ETL next door.
(Except for white colonies in SA and Rhodesia, who might go along better with ETL than London).
For the same reason, the British won't want to let go of Africa.
First, they will badly need markets, raw materials and manpower, to offset the loss of Asia and of European markets, and to match the ETL power.
Second, they won't risk their colonies being taken over or falling under ETL influence.
So, we might see lots of goodwill both on British and native sides in Nigeria, Kenya, Tanzania, Uganda.
White dominions might go either way. Rhodesia and SA will likely gravitate around ETL, or play ETL and Britain off each other. Australia and NZ can either tighten the links with UK (to deter Japan), or fall into US sphere. Canada will likely join US sphere.
Regarding African ETL colonies, they will probably not gain independence or autonomy for decades, if ever. The Axis powers won't hesitate to use carpetbombing, bio and chemical weapons, deploy tank divisions...
They have full military and logistical cooperation against any rebellion.
They also have the aura of winning the war, there were no Allied landings in Axis/Vichy Africa. The USSR will soon be no more. China will be too weak and focused on Japan. The USA won't have the will (for a long time) to oppose ETL colonialism, beyond (at most) words.
In fact the only country that is really in position to escape colonialism (from Britain, Japan and ETL) is India. And even there, outside powers might fight by proxy, sparking a messy civil war.