An autopilot in busy airspace is a must to have for a serious IFR pilot. Flying around the LTMA under London Control, getting ATIS, preparing plates and approach briefs is not the place to be wandering off heading/height while you are distracted even for a few seconds. You want to play with the big boys you play by there rules and they do not hand fly.
I flew into Gatwick without an autopilot...although the approach and nav was very straightforward.