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If there’s no wobble there’s a good chance it’s the freehub, which could be loose or could be knackered. If you’ve got the tools you could try and loosen the freehub a bit then tighten it back on, see if that solves it (would recommend against just tightening first as it’s easier to over-tighten that way).
If knackered, it depends on the type of freehub you have whether it can be serviced or only replaced.
http://www.whiteind.com/freehubbodies
Seems White use Shimano hyper glide c or micro spline free hub bodies, with pawls instead of a centrelock. Centrelock are meant to be replaced (despite being on some Dura-Ace hubs and costing £150). If it’s got pawls it might be serviceable.
Hope that helps.
Thanks for the response.
Have had another look and I think 2mm is an overestimate. No independent movement in the cassette cogs and it’s on pretty tight so assume it’s the freehub. Is that likely to be serviceable or a sign of a freehub that’s passed its best?