Paul,
The man said 'peristaltic' pumps. Like in dialysis machines, printers, dosing pumps etc etc. Sadly, they are not typically intended for use as fast or high volume pumps.
OP,
I can only think that a centrifugal pump / impeller pump with a clearance between impellers and housing would be the way to go. These are the usual pumps for bilge and general purpose and I have seen these with maximum particulate sizes up to 3mm or more. But now I am assuming things about your application and answering my own assumptions which may not be helpful. So if you can fill me in; how much water do you need to move? How far? How high? Particulate size? Nature of contaminates? (acidic/alkaline?) Impeller pumps can be a bit violent, is that an issue? Impeller pumps are also not self priming, is that an issue?
PE