You have to ignore any information about it being a faulty washer .. how can a washer have any effect within a tap that is always in the open position.
If the washer in a stopcock leaked, you would never be aware of it. Think about it, the washer is contained inside the tap body and if it leaked, it could only leak into the main supply pipe.
Now you have added that little snippet about it leaking after you tampered with the cistern feed, it's obvious what has happened.
Stopcocks have a habit of leaking through the spindle.. ever so slightly.. and
when this happens they usually seal themselves up with calcium which is present in the water. They will sit there happily, often for years on end and never leak again due to the calcified ring that has formed around the spindle..( It is a green/white chalky substance often damp. Green comes from the copper pipe and white from the chalk)
So it's a simple DIY fix in 2 minutes. If you replaced your cistern feed, then you can easily do this. Watch the video shown above in Buenchico's post.
.. good luck.