You would think with 4 engines on a relatively small plane that the VC10 could have carried more fuel, so it wouldn't have to land so often.
One of the reasons for so many stops was that the aircraft in those days had a relatively limited range.
Of course the main reason they stopped so often was not for fuel, but because that is where the pax wanted to get to. LH was more operated like a bus route in those days. On the 707 we frequently did LHR-FCO-Far East, or Karachi Rome Frankfurt London. Short sectors done by an aircraft that could stay airborne for 9-10 hours.