In an earlier contribution to this discussion,
NikV wrote:


Our dishwasher is in the position the OP wants the washing machine.
The waste standpipe (with trap) is in the void behind the cupboard
next to the machine, it then runs behind this and the next cupboard
into the corner cupboard where it goes down into the void behind the
plinth and runs through this void (use a hole saw to cut holes in the
cupboard sides at lower and lower points) under the built in gas
cooker until it exits the wall and elbows into the foul water gulley.
The water supply runs right behind the kickboards in U shaped cutouts
into the plinth. It involved pulling out the two cupborads next to
the dishwasher and doing the cutouts for the waste and mounting the
standpipe and trap, the rest was done in situ.

That's fine - and is basically what I was suggesting that the OP should do.
The basic difference between your setup and what the OP originally wanted to
do is that yours has a continuous fall on it, and exits the house at low
level rather than being brought back up to connect into the sink trap.
--
Cheers,
Set Square
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