How can I drain washing machine into toilet cistern downpipe?

I've a toilet with separate cistern to bowl, so has a 2" (?) downpipe from the cistern into the bowl.

I would like to setup a washing machine nearby and wondered if I could drain into that downpipe with a tee-connection? I'm happy that washing-machine suds/water will appear in the bowl. But I'm concerned that if I flush the cistern, would it force water out into the washing machine?

I can't tap into the soil-pipe as it's clay and I really don't want to disturb it.

Nearest waste-water is two rooms away in the bathroom, so not so easy to get to.