"We landed on the available runway. Unfortunately it was a little too short.
What's seen in the Leeds incident is a matter of luck. Yes, it was a little too short. That everyone survived was luck. Continuing to post popular press renditions of aircraft mishaps is entertaining, but contributes little to a technical discussion of the facts. That the passengers on board thought the pilot was a "hero" for the successful outcome is nice...but meaningless. Imagine what the families of the deceased might have thought had he failed in his efforts. Equally as meaningless. He was lucky.
What actually happened...
The HS-748 was cleared for a runway 23 take-off at 23:29. The first officer was the handling pilot and the take-off was to be made with full dry power; the water methanol system was selected to standby. At an airspeed of 111 kt the Commander called 'vee one, rotate', the first officer moved the control column rearwards and the aircraft became airborne. Less than five seconds after the 'rotate' call, at an airspeed of 115 kt and a height of between 30 feet and 100 feet agl, the no. 2 engine suffered a catastrophic failure resulting in a sudden loss of power and an immediate substantial nacelle fire. The aircraft yawed 11deg to the right of the runway heading. The Commander took over control and the crew were told by the senior cabin attendant that the right engine was on fire. Engine power was reduced and the aircraft yawed 14.5° to the left of runway heading. Four seconds later, the sound of the engine fire warning bell was recorded. The aircraft was in the air for a total period of 27 seconds before it touched down.
The aircraft ran off the end of the runway at 62 kt., crossed the perimeter track and came to rest with the collapse of the nose landing gear.
In another case the crew had no choice but to reject above V1 because of locked flight controls. The aircraft received substantial damage in the ensuring rejected takeoff...another illustration that rejects above V1 don't go well, and that it's not nearly as simple as "pulling back the power and applying brakes."