I know it won't seem like it matters but you can launder£5. The lowest amount that I know of which, following the investigation and tracing of the money trail after a successful terrorist atrocity, is £20 which was "washed" through an electronic gaming terminal and which then paid part of the rental of a car to the destination.
The min turnover, be it 1, 2 or whatever x is just to protect the casinos should any money used in terrorist financing be found to have gone through a casino.
The have to have some system, compliant with AML legislation, to show they are not allowing even inconsequential amounts to be laundered.