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I'm fairly sure 4x2@16" is also what I've seen here, when the upper floor of my house was being built (prior to plasterboard going in), and again when contractors partitioned various rooms at work - I can't imagine UK and US standards being very different.
The single shed I designed and made (#notanexpert) was on a very low budget, and only has to keep the weather off a few garden tools - if I wanted to keep more valuable things (e.g. bikes) secure I'd probably go for a heavier construction.
At a practical level, if I'd used 4x2" at the closer spacing each frame would weigh around five times as much, and I wouldn't have been able to move them without help.
@Backstop - compromise on 2x2@20" and claim it's based on an obscure local standard?
4x2@16" is the default in the US for all studwalls. Check your tape measure, every 16" the numbers are different colours for a reason. So you can mark out your spacing on the top and sole planks easily.
Probably overkill for a shed. But it's what I'd do.