something similar happened to someone I know, except in Tower Hamlets. They phoned TRACE, only to be told the vehicle hadn't been towed and were about to report it stolen, but just beforehand asked a security guard in a nearby building if they could view CCTV footage of the street. Lo and behold Tower Hamlets parking enforcement van towing the vehicle away in glorious technicolour. It took them about 2-3 days to admit they had it, at one point they said they may have had it but lost it. After much detective work at various car pounds, he found it, but.. it gets better, they had dropped it onto another vehicle and damaged it. They then charged him a 3 day storage fee (even though they hadn't admitted they had it until then) and would only accept a credit card payment, causing even more hassle.
I wish I could be as incompetent as that in my job and get away with it.