In reply to Jim Lancs:
Watchgate can put water into the Thirlmere aqueduct, but it can't treat water from Thirlmere as its a few tens of metres above it, without a pumping station!
And the usual state of play is that it doesn't, it just send its water down the Haweswater Aqueduct.
Fun fact, it can also treat water from Windermere, and Ullswater can be used to top up Haweswater (both scenarios are pumped). These are later additions to the system, to improve ability to meet demand.
Getting back to the question by OP.
We can't tell if waters safe to drink just by looking at it.
Brown water can be safe. Clear water can be safe. Either colour of water can also be unsafe. The world is full of many different kinds of exciting dangers, and we can't see all of them.
The higher likelihood, maybe lower consequence (but also potentially nasty) risk, somewhere like Kinder, is some tummy bugs from other people or animals. A decent, new filter should be fairly competent at removing.
The lower likelihood, higher consequence things to worry about might be something like a gamekeeper has just dropped a tub of rat poison as he crossed the beck upstream. Your filter will not help with chemical nasties.
Brown indicates that there is something in there other than pure water. But there is plenty of brown that will not do us harm. Just like I could see pink water and be certain it is more than just H2O but not know if it is antifreeze or blackcurrant squash.
From the description though, I think I'd be happy taking the chance with either of those sources after putting it through a filter. It sounds like you were still fairly close to source where the water has had least time to encounter something nasty.
Clearly, nobody can guarantee it though.