It would be highly illegal - all jumps away from a dropzone require a display permission.
Individual aircraft used for parachuting need to be cleared for it (usually mods are required - taking out seats, doors etc) but an AOC is not needed for parachute operations - I think you can use a private category aircraft with a ppl (providing you don't pay him).
The operators are cleared by the CAA but that is in respect of the dropzone and their operations manual, which is based on the BPA's ops manual if they are a BPA approved dropzone.