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used a lot of these for getting floorboards (relatively) level:
https://www.screwfix.com/p/broadfix-plastic-flat-shims-assorted-60-pcs/798KJ?kpid=798KJ&ds_rl=1249413&gclid=CjwKCAjwg-GjBhBnEiwAMUvNW2SgR99ithfkGsB2_PWCTcZXNiPoDXsSJFoVhM6V52pY1yyXjS8nwBoC5MoQAvD_BwE&gclsrc=aw.dsmore work - but could take up the boards and then use 18mm (maybe 25mm even) marine ply atop the joists.
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Depends on expectations / how perfect you need it but Sheet Lino is pretty unforgiving of less than perfect subfloor. I wouldn’t use anything less than 18mm over very well levelled (ideally freshly sanded boards). Any joins between ply sheets need careful attention to stop them showing - so lots of fixings and filling and sanding. Check the marmoleumn data sheets for installation. They might even say use a latex self level screed over the ply. …..So I’d be concerned about shims and 2mm ply personally !!
I'm laying a new ply subfloor for lino in our bathroom, the floorboards underneath are pretty lumpy and the 2mm ply I'm taking up is flexing over the voids. Is there any clever stuff I can use between the ply and the floorboards to fill the voids, some of which are up to 5mm? Or would I just be better off with thicker ply instead that can span the gaps with less flex?