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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.
Aroogah-
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?
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You're quite right about the different colours on the tape measure.
Having used the same tape measure for 30 years, I hadn't noticed - I had to go and check.I find this worrying.
MrE
The frames on mine are 2"x 1" at 24" spacing, and assumes the T+G cladding contributes to structural stiffness. Built as four 'wall' frames, assembled in situ by screwing the frames to each other, with the roof assembled last. Admittedly it's in a sheltered position, but has been fine for the last 20 years - pics on pages 267 & 268.
4x2@16" sounds like the sort of stud wall that will hold another storey above it? Doubtless conforms to building regulations but perhaps excessive for a modest sized shed?