This is a pretty good summary, for its length, but of course there was also a lot of politicking involved. Defeating Richard was the apex of the conquest, but it wouldn't have happened, nor would it have lasted, without support from enough of the lesser nobility (along with a fairly absurd claim to the throne by descent).
If you want to get into the details, Dan Jones' books are amazing. I would recommend:
The Plantagenets: The Warrior Kings and Queens Who Made England
and
The Hollow Crown: The Wars of the Roses and the Rise of the Tudors.
The latter would cover the period about which you're asking, but would probably make a bit more sense if you started with the former. I read them pretty quickly at bedtimes and didn't absorb as much as I would like to have, but the saga is well-told and the personalities come to life. Quite entertaining.