It doesn't take long to find out via Google...
Basically, the first few (pilot scheme) had a single prime mover of the same type as the D600 Warships (which had two), i.e. NBL/MANL12V18/21BS.
For the production series, D6306-D6357, the engine was uprated from 1,000 bhp to 1,100 BHP, the idea being that two of the "Baby Warships" would be equivalent in power to a D800 series Warship -given the 75mph maximum for a D6300, this would be rather pointless on express passenger trains. (Traction and braking performance would, in theory, have been slightly superior due to more wheels on the rails.) The NBL Warships had two of these prime movers, so if you can get a recording of one of these locos running on a single engine, you are done and dusted! (The preserved Warships are Swindon, are they not?)
(That bit didn't take long. The following took some tracking down - it is 30 years since I studied German!)
Some of the German V100.10 (class 211) locos had MAN engibnes of this type: not sure which or indeed how many, but basically the SWD DCC sound module is the V100 with Desilux horn and assorted other British sounds. This means it could be a Maybach recording instead.