I flew into Gatwick without an autopilot...although the approach and nav was very straightforward.
You flew in VFR. Try going in from the airways, getting ATIS, preparing plates etc.
I am saying that learning the IFR 'trade' in a badly equipped aircraft in busy airspace is not the brightest of moves. Dead reckoning or using unapproved equipment is not very sensible.
IFR is a highly skilled game requiring proper planning and use of all of the tools possible to ensure it is carried out safely.
The average club hack with a single VOR that is not FM immune etc is not an appropriate platform. Not to mention the fact that VOR reliability low down patchy at best. So relying on it in IMC is daft, just imagine bowling along through Luton or Stanstead and the VOR loses lock. What happens? You have to declare an emergency, get a controller to divert resources to sort you out.