How to fix a leaking stopcock
The stopcock controls the flow of water in your house, shutting off the entire supply in an emergency. If you discover a leak from your stopcock, then you should tackle the problem immediately so that the problem doesn't escalate.
If you're absolutely sure it's the stopcock that's leaking then you might be able to repair it yourself, however be prepared to call in a professional plumber if you have even a shred of doubt.
Tighten the compression nuts
First you'll need to locate your stopcock. It's usually found under your kitchen sink or under your stairs. If that's not the case, it will be located at the first point of entry of water in your property, for example, your downstairs toilet.
If water is leaking from the compression nuts, these are the nuts that secure the stopcock to the pipework, you should first try tightening these. The nut on the body of the stopcock seals the packing into the gland which stops water leaking through the spindle. Tightening this nut will often stop the leak. Take care not to over-tighten as this restricts the stopcock's ability to open and close.
Replace the gland packing
The problem can also be caused by the gland packing wearing out. To fix this:
Buy some gland packing or PTFE tape at your local DIY store.
Turn off the water supply externally, i.e. at the pavement or on your boundary
Unscrew the gland nut anti-clockwise.
Pick out the old packing with a penknife.
Replace it with the gland packing or PTFE, wound clockwise around the spindle.
Pack it down and retighten the gland nut
Open the stopcock fully and then turn back half a turn. This can prevent it from seizing.
The stopcock should now operate firmly, not too easily, and be leak free.