The Dylan song ( "She belongs to me") by the Nice mentioned some way above was not a whole LP side as it was on side two of "Nice" with "Rondo '69".
However, "Brain Salad Surgery" by ELP started on side one of the LP with the same name and also took up the whole of side two. Oddly the track of the same name on "Works" does not appear on the LP.
As regards 45s, the Nice had "America" which was nearly as long as "Hey Jude", and then there was Fleetwood Mac's "Oh Well" which took up both sides.