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Another point is that can the drain pipe be in a 'U' shape? The
pipe drops from the washing machine, under the floor and then rises up
and connects onto the 110mm WC pipe. Water will be trapped in this
pipe.

Washing machine pipes are always full of water.

I really think you're making this more complicated than it needs to be.
If you're in any doubt about whether the washing machine pump will cope,
make a mock-up with a length of 32mm waste pipe laid on the floor and
you'll see it'll cope no trouble.

--
Skipweasel
Pay no attention to that man behind the curtain.