I've been having a look at various places in Central Scotland to desense, and the best place I've found so far is The Centre in Livingston. It's a large linear shopping centre with four public toilets, of varying difficulty. You can walk back and forth between them, and cross over the road into the neighbouring Factory Outlets to use the large toilet in there.

The easiest toilet in The Centre has the urinals screened from the sinks, in two separate rows, with large dividers in between. The most difficult has a small row of urinals with mirrors and sinks behind them. Ideal for solo desensing.