Hi Again,
Some good links there. Yes, use any method you have to take the water, ex the washing machine into the cistern. I chose 65+L as the minimum cistern size as you say this is how much goes through the washing machine in one cycle. The grey water then passes through the home brew (but widely used) filter via gravity, in its own sweet time. Even if things are slow, you should not lose any. A large bore overflow 32mm+ to your houses drainage system should keep you from having any less than happy moments.
I would attempt to use the ex washing machine water as quickly as possible, not letting it hang around for extended periods, especially in summer. I would also keep both systems as cool & dark as possible.
I would not be making the sand bed 1M deep for your use. Slow sand filtration when used commercially is aiming to eventually supply the water to you & I.
I would make it a sensible depth & do some trials. The Hockerton people seem confident enough to bath in it, I wager there are more stages

I am unsure of the relative height of the washing machine in relation to the proposed filter or IBC but gravity would keep things cheep & reliable.
Have fun. Andy