It were'nt only the British. Everly leading European nation of that time wanted to have colonies. At it's height was the Berlin Conference in 1884 where the European nations decided who had rights to which part of Africa and which was free to be grabbed (the Belgian king got the Congo region quasi as his private property).
One ostensible good thing that came from that conference was the dicision to end the slavery then practiced by african and islamic cultures. But one could argue that they replaced it with enslaving the whole continent ;)
So, yes, African history would have been different without the Europeans. But Northafrican history would have been different if the arabs hadn't invaded in the 700s. There's a lot "what if's" in history.
The British were once just as primitive as Africa was. There's no reason whatsoever that suggests that Africans wouldn't have developed.
We may not have figured things out as fast as they did but I assure you Africa would have caught up eventually.
Evolution takes place regardless of what race we're talking about and the same kind of curiosity that caused the likes of Isaac Newton and Thomas Edison to make their discoveries would have most definitely sprung up in Africans.
Also, Egypt is widely regarded as one of the cradles of civilization itself and guess where Egypt is located....yup, you guessed it, AFRICA!!!
It's not a matter of whether or not Africa would have developed, the question is when.