Hello,
afaik the first Carriers come 1936 to the british forces, 1940 their french adventure was done. At this time the british army get 4 diferent models of the carrier for Bren MG, Vickers MMG, Scout (radio), and cavalery carrier (up to 6 soldiers) . In one book, I found a picture of the captured carrier T 8288 and T 8313 (north africa) all MK 1. The production of the MK. 2 starts afaik 1940.
For 20 mm (1/76 // 1/72) PSC make a nice kit (3 vehicles & crews), sone they bring a Loyd carrier (a box with 2 vehicles ,crews and 2 at-guns). The Loyd Carrier will be another canidat for your troops.
Hope, this can help you a little bit, Sebastian