This locomotive was built by Peckett in 1948 to their 'Special R4' design (differing from their 'Standard R4' in that it was built to a smaller loading gauge). It was not delivered until 1952, to Croydon 'A' power station. It did not stay there long, however, and was soon sent to Croydon 'B' power station. Here it joined its sister loco No. 2104, which also spent a period at Quainton before moving elsewhere, and Peckett 2103 (part of the same batch).

In the late 1960s, diesel locomotives took over at Croydon but No. 2105, along with No. 2105, was kept as a spare until 1972, when they were put up for sale. Purchased by a QRS member, 2105 arrived at Quainton in December of that year. It has now had a major overhaul and in 2002 is operational, renamed Rokeby.