Hi Alec,
If your vehicle was demobbed from TMP Thatcham, that means that it would have spent the last part of its service life there, but for how long. TMP is Training Materiel Park, a bit like a van and truck hire centre, when a unit requires more vehicles for a scheme, to stand in for one off the road, etc, they were drawn on a loan basis from TMP. This means all kinds of units may have had it for a short time, but the would not have applied their unit markings, at least not normally.