If the basket and pre-filter/ one way valve are installed, this should stop most of the larger foreign objects.
Things like muddy/sandy water are a different story - likely to put excess stress and wear on the pump housing and impeller(s) when compared to pumping clean water. Fire pumps have to be designed to handle this type of water on some occasions (i.e draughting from creeks or dams, however extended operation in flood waters is likely to send your truck off for a pump service sooner than you may have expected.
You're right in saying that there are sludge pumps designs specifically for pumping this 'dirty' water. However in a situation like Stockport, any available pump goes and you have to make do with what's available.