No HAPs between Folkestone and Dover, they (and anything non-corridor) were banned in the narrow single-bore tunnels there. They could get to Dover via either Canterbury or Ramsgate. The through trains from London to Dover by all routes were pretty wholly just CEP.
I never encountered an MLV on a normal passenger service but they were used on parcels services, on their own or with trailing vans, and also even on freight. A real oddball duty was in the heatwave and water shortage summer of 1976, washing trains was banned at Ramsgate depot, until someone remembered BR had their own old well near Folkestone; some retired milk tankers were resuscitated and a pair of MLVs hauled them every day to Ramsgate depot washing plant.