Hi Colin,
No, regardless of whether the camper is used privately or commercially, it needs a Commercial Vehicle Roadworthiness (CVR) test, not an NCT.
For campers weighing less than 3,500kg it’s a light commercial vehicle (LCV) test and it’s a heavy commercial vehicle (HCV) test for campers weighing more than that.
Go to the official Commercial Vehicle Roadworthiness Testing website (by the RSA) for more information.