Check your tank in the attic, if it's a galvanised tank it may be rusting away turning the water brown. If its an old pvc tank maybe a lot of sediment in the bottom of it needs cleaning out.
You would have to tie up the ball cock in the tank, thats the bar with the ball on the end of it that floats on top of the water. Tieing this up stops that tank from filling up. Then you would have to run all the cold taps in the bathroom to drain the tank. Then its just a matter of getting rags or cloth to clean out any muck thats there. When finished untie the ball cock and let the tank fill up as usual.
Had a similar problem a while back and it was caused by dirty water from the heating system getting into the clean water inside the cylinder. Had no option but to have a new cylinder fitted.