When tried using previously drawn water, with some heated in the kettle it's worked out at 6-10 litres for the washing, plus some extra separately for several rinses of the cloth.
It will be more for doing the whole thing the usual way at the sink straight from the tap, though never measured for obvious reasons. (Tap always switched off when not running the cloth under it.)
This is 2019, not the 1850's!
That archaic side of it actually makes it enjoyable for me.
Plus, as I no longer need to wash my hair every day, it's useful not getting it wet. (When I was younger and it was horribly greasy, I really had to wash it every day.)
And I've always hated baths.
Water bills now show my usage as consistently about 1/3 of the standard consumption.
Years ago with the same water company, when I was living in a flat with a power shower for the first time, one of the water company staff suggested when I queried the bill that there might be a leak as I was using so much. The building manager checked, and there wasn't, so it must have been all the long power showers. Though I've also rationalised other things since then, like having clothes that can all go in the same wash load, other than a few hand wash items.