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Do I need to shim the parts?

My parts are cut from 6mm un-laminated MDF, I've sealed the pieces and started a first dry fit, the slots cut in are 7mm giving me a 1mm gap all round the slot.

As the cutting is so accurate, would I be better putting in some 0.4mm birch shims to fill the gaps?

here's my thought on this, I wouldn't worry about the those gaps to much, as they don't effect the flatness of your build surface. What i would worry about though, is the vertical tolerances of those pieces. check to see if they are the same height. If not they will throw your build surface out of wack when you go to assemble your base.

someone in the uk may have cut your frame from the wrong file, melamine is slightly thicker than plane mdf, I think if they used the acrylic version, which is closer to 1/4" in thickness; you would have better tolerances. another note: thickness of mdf varies from different suppliers/manufacturers. its important that the person laser cutting these parts know what thickness they are using to have correctly cut product.