Why not just level the floor locally, to create a little plinth for the sink and mashing machine to sit on? Knock together some shuttering and fill with concrete. You’ll be creating a ‘wedge’ of concrete, and with a washing machine vibrating away on top it may attempt to travel down the slope. To counter this I’d drill two or three holes in the floor, along the width of where the plinth is going to go, and stick some short lengths (100mm) of rebar in. Say 50mm deep holes, with 50mm rebar sticking out. When you pour the concrete the rebar will be covered, and these pegs will anchor the plinth and stop it going anywhere.
Like this naff-tastic Word-art technical drawing:
[/url]Plinth by W Hyde[/url], on Flickr[/img]