(This assumes you have a suspended floor on joists)
Is the slope in the joists or just in the random stuff on top?
It sound like you have a bit of random crap there and a smallish room, so why not - it won't cost much whatever you do.
For a small room, I'd take the boards off and reline with heavy water resistant ply >= 18mm, screwed down.
18mm should give an excellent base for plastic coverings and lino and may be sufficient to support solid tiles with the correct flexible adhesive and grout (depending on joist spacing, may have to jump to the next thickness up of ply).
I'd silicone bewteen the ply and between the ply and the wall too - another line of defence against accidental water spillages.
MMM joists are a, as yet, uncovered hotch potch of timeteam hard as F oak and recent softwood infills (old stair well now floored over to "match" (but even less level - thanks profeshunals))
I'm not much of a carpenter. I wonder if you could shim the joists with planed tapers on top? Bit tedious but once done it would be solid.
400mm not a problem, 500mm should be OK unless bath on top (cross bearer heavy planks; eg scaffold planks; under the bath feet perpendicular to the joists are a classic solution here), 600mm getting a bit bendy and I personally would be looking at 25mm or whatever the next thickness is unless it's in an area with low point loads.
was thinking to pack here and there, screw down then expanding foam (thru drilled holes) to support in between screws, rather than attempt to wittle away "perfect" shims etc - whaddaya reckon?
I think the dynamic load (pounding) will destroy the foam over a short time. It's an OK "bodge" for static loads, like firming and sealing windows in, but I have a bad feeling about foam structurally on floor joists.
Having thought about it, if you just screw and glue 20mm PAR[1] along the top of the joist, mark a level line along both sides with a long spirit level and power plane down to the line, it shouldn't be too arduous to shim the tops. Obviously remove and further sink any screw heads you are getting close to as you go (countersink them with educated guesses to start with).
If you can get within a couple of mm overall, it will be as good as anyone else's joists and rather better than what you have now.
[1] Or be smart and switch to a thinner wood like 12mm where that would be sufficient, then maybe down to nothing if you have a section that's about right anyway (hint - you're allowed to plane the joists too, oak and rusty nails permitting!). An electric plane will make short work of removing that amount of material IME.
Another job for body filler IMO. Get the level with a length of 2" x 1" with a piece the thickness of a board fixed to it, grease the underside, pack out with filler, remove the batten, and you have perfect supports for the boards. A 3.5 kg tin from a trade place shouldn't be more than £15.
I can see the pros in both the wood and body filler approaches - I think it will depend what state each joist is in as to which I will use where - on the new joists, Tim's "power plane PAR in situ" sounds most straightforward, on the (I expect) old nail infested oaky bits (which will probly twist a fair amount too), I may well try Stuart's body filler trick.
For the new boards - what spans is 18mm chipboard good for? assuming it is drenched in thinned polyurethane varnish, will it be anywhere near 18mm ply for performance & esp. longevity?
Prob I can see with ply is altho it's a small room it's an awkward size so I'd have to cut ply 8 X 4s down and have a fair few joints - with flooring chipboard as least the "built in" t&g will help on the joints....
IME chip isn't as robust nor quite as stiff as WBP ply but it is adequate. With chip I would go over it in exterior stain or diluted varnish to both add a little more water resistance and to improve the ability to stick lino down to it.
Better do it without the screws, just glue it. Weights on it while the glue sets, and leave it overnight so its good and strong, since youre planing it down to nothing.
Hmm, I think I'd tear that up and shim it - calculate height and shim every 30cm or so. Put thick ply down over the top, then backerboard, seal at the edges with silicone, then ceramic tile on top. I don't like lino because it can split and/or soak up moisture if it gets wet at the edges. I think I'd tile it a couple of inches up the wall all round, too.
If you don't like the cost of ply, chipboard would probably do (so long as moisture never hits it! :-) so long as the joists you're putting it down on are pretty close together (I'm just doing a floor this week with chip, but I'm putting in joists on 12" spacing underneath rather than the
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