OK, here is what I did, in case it helps anyone.

I was persuaded by the "management", that I didn't want the varnish to
change the colour of my sanded pine floorboards. However, I did want a
matt finish, and didn't want the plasticky finish that my experiments
gave with water-based satin, so this is what I did:

Hoover, wipe down with white spirit, allow to dry.
Two coats of Ronseal Diamond Hard satin (water-based polyeurethane).
Before final coat - Light sanding, Hoover, wipe down with white
spirit, allow to dry.

Three coats of Wickes Professional matt varnish (solvent-based
polyeurethane).
Between coats - Hoover, wipe down with white spirit, allow to dry.
Before final coat - Light sanding, Hoover, wipe down with white
spirit, allow to dry.

(The constant hoovering and cleaning is down to the fact that the hall
had to be in light use between coats (the Wickes tin advises 16-20
hours before re-coating).

The result is a pleasing clear matt. I did the whole job with a brush,
so there are some brush marks in the final coat, which I may remove
with wire wool when it's fully hard.

I'm pleased with the result, which has given what I hope is a decent,
hard finish, without significantly changing the colour of the wood, as
I would have done had I applied solvent-based varnish to it directly.

I say "significantly" - I think the solvent-based varnish has deepened
the colour ever so slightly, which suggests that some of the effect of
this varnish on wood is due to the way it reflects the light, though
the effect mostly occurs when solvent-based varnish is absorbed by the
wood, which I have avoided.

A poster in another thread suggested that multiple coats of matt
varnish would give an opaque finish, which I didn't find to be the
case (though perhaps the reference was to water-based matt; not that
I've seen any).

Obviously I can't comment on how hard-wearing it will be, or whether
there will be issues with one kind of varnish on top of another. With
five coats in all, I'm not anticipating issues.

Regards
Richard