Looking at the barbets plate in Collins Field Guide to Birds of Eastern Africa, there are only two barbet species that have the black and white colouration as is shown by this bird, those being spot-flanked barbet and black-throated barbet. Then looking at the second picture (attached above), there are no spots visible so I think it has to be black-throated barbet.
Thank you all for the idea of it being a barbet, I never would have though of it being a barbet at all, I always thought of barbets as larger and quite colourful birds.