Nice BG and pose here. I agree with you that many common birds are often overlooked! You are right about the white patch. In the future, try to have the light coming from behind your shoulder, it should make the bird easier to expose(the darks and lights are tricky in this sidelight), and check the histogram.
I agree, the Great Tit is very difficult to expose because of the white and the black colors in the head. Next time try to catch them in a more natural perch...