Yes, you can run the dishwasher and the washing machine off the same supply by using a connecter with two outlets. We used a brass one because the plastic ones leaked.
The washer will drain in a u shaped drain but the dw will have a screw on drain, I forget how we connected that but dh sorted it and he is no plumber so it cant have been that hard.
Even if you run them both together they wont drain at the same time and the dw wont use much water, probably 10l compared to a washers 50l.
I think the water companies should stop fannying around with tap inserts and save-a-flush's and supply subsidised dw instead. There's huge savings to be had.
Spotty I hope you do just that. You've got years of this otherwise and the kids will use lots of plates when they are teenagers and have loads of friends round.
I bought a Miele dw in April but never mentioned it because some of you were having a rough time of it so I didn't confess. It's a brilliant machine though because it only needs to run every other day and it tells me how much water and electric it uses after the cycle ends. I got £370 off it buying it off a builders merchant and used my Yorkshire bank switch incentive towards it too.