So I want to have a dishwasher and washing machine in the same room.

I see that you can get a splitter for the inlet:

http://www.amazon.co.uk/Brass-washing-machine-Y-piece/dp/B008TN6VYY/

And for the outlet:

http://www.amazon.co.uk/294/dp/B005CTSA4W/

Has anyone done this? Can you run both at the same time (don't think I need to).

This is a good thread.

Any other plumbing stuff?