The Boulton Paul P.125 was a jet version of the P.108 Balliol, designed to replace the Percival Provost, but that didn't enter production.
The Percival Provost was a basic trainer that had replaced the same company's Percival Prentice. At the time the training route went from the Provost to the Boulton Paul P.108 Balliol and then onto operational jet aircraft. In 1951 the Air Ministry decided to change to an all jet training system. A replacement was thus needed for the Provost.
Boulton Paul submitted the P.124 and the P.125. The P.125 was a conversion of the Balliol that would have been powered by the Rolls-Royce Derwent jet engine. The original design for the Balliol had specified a turbo-prop engine, so this wasn't a terribly dramatic change. On the P.125 the Derwent replaced the Rolls-Royce Merlin in the nose of the aircraft, and the exhaust pipe emerged below the rear fuselage. The P.125 also got a nose wheel, offset to port to keep out of the way of the air intakes. The P.125 was given four fuel tanks, one in each wing, one in front of the cockpit and one behind the radio set.
The P.125 wasn't accepted for production, and instead the Jet Provost was chosen.