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