Recently moved into a basement flat in a victorian terrace. Having real problems with drainage in the bath and sink, and I've tried all sorts of unblockers which haven't helped. Seems that water drains slowest in the morning and evening, so I'm wondering if it's linked to how many other people in the building are using water?
Anyone know if this can be sorted? Or anything I can do to ease the problem?

If it's not a blockage problem and it really is causing you trouble, you could fit a discharge pump. No idea where you'd get one from though as I only deal with industrial units.

something like a diaphragm pump should give you enough punt and be able to take soft solids too.

You could try looking at the MHs and seeing if they're full of "waste product". Further options will become immediately apparent.