If I interpret your location correctly traffic heading south over you would turn in for a 4-5 mile final, which isn't desperately tight for smaller aircraft. As has been suggested, you probably saw aircraft on visual approaches where the turn on is entirely at the pilot's discretion - and some could really turn in tight!!
Way back in the Golden Days a Heathrow controller bet a Viscount pilot coming in via Watford that he couldn't land on 28R without receiving the ILS Middle Marker (which was about 1.5 miles out I recall). The pilot accepted the challenge..... and the controller had to get his wallet out later!