An aircraft design needs some sort of propulsion and often the succes of the design is heavily dependent on the chosen engine type. For the VC10, Rolls-Royce was able to supply one of the first turbofan designs, the Conway.
Designed by Alan Arnold Griffith, the R.B.80 Conway design goes back to proposals from 1947, with the original experimental bypass engine using both Avon parts and segments from another experimental design. It evolved into a two-spool bypass turbofan engine labeled as the RCo.2 by the Ministry of Supply, but was only tested for a mere 133 hours as the intended user, the Vickers Valiant low-level Pathfinder, was cancelled. The RCo.5 did not fare much better, being designed for the still-born Vickers 1000 design. The design was saved by the Handley-Page Victor B.2 which used the RCo.11 version instead of the B.1's Armstrong Siddeley Sapphire engines.
The civil market first encountered the Conway when the RCo.10 and later RCo.12 version was ordered to power TCA DC-8s and BOAC 707s, amongst other orders. Unfortunately, this segment of the market would later collapse when Pratt&Whitney countered with the JT-3D version of their DC-8/707 powerplant. As the first turbofan, the Conway offered a significant improvement over the pure turbojet designs, with a lower fuel burn, but the JT-3D went for a larger bypass ratio and trumped the Conway's numbers. Together with further development of the 707 airframe, it would lead to a more economical design for the airlines.
For the VC10, Rolls-Royce evolved the Conway engine design into a 21,000 lb (94.1 kN) thrust engine by increasing the bypass to 60% alongside other revisions. It kept the, for that time revolutionary, internally air-cooled turbine blades and associated high exhaust gas temperature. This was the RCo.42 that would power the Standard VC10s, also referred to as the Conway 540.
The RAF's hybrid type 1106 version used a slightly different version that was labeled Mk.301, providing 21,800 lb (97.6 kN) thrust. Basically this was a Super VC10 engine with some small changes to comply with the RAF's demands.
For the Super VC10, the final development was the RCo.43 variant, which delivered 22,500 lb (100.1 kN) thrust. This version was also known as the Conway 550, with the EAA Super VC10s using Conway 550B engines.
Several Conway engines have been preserved. This goes back to the drawdown of the British Airways VC10 fleet, when BA apprentices prepared several ex-VC10 engines for display. I suspect that they mostly used RCo.42 engines for this purpose as all the RAF variants would continue to use RCo.43 engines, re-labeled to Mk.301 Conways. No doubt this list is incomplete, so let me know if I need to add one or more engine(s).