OK, that's perfectly normal.
If you want to clean the tank, which is entirely up to you, you need to turn of the water supply to the tank so it doesn't keep filling, and then drain the tank via a cold bath tap / flushing the loo.
You can figure out which cold taps etc come from the tank, by turning off your main stop cock, and running the cold tap and seeing if the water stops (directly from the mains) or keeps running (from the tank). The cold tank probably holds about a bath full of water, it's not a huge amount you'll be wasting.
Then you need to get in the loft and scrub the inside of the tank / the overflow / anything else that looks grubby. You'll probably now have a small amount of murky water in the bottom of the tank. You can mop that out with old towels or push it out the outlet to come out of the bath tap.
Have someone turn on the main stop cock for a little while so some water comes into the tank, use it to rinse around any dregs and flush that out the outlet to come out of your bath tap and if there's any remaining mop it out with an old towel.
Turn off the bath tap, turn on the main stop cock, put the lid on the tank. Finished.