Most stopcocks and gate valves are rarely used. Consequently they can become jammed. The best thing to prevent this happening is to close and open them at regular intervals to prevent them seizing up.
If the stopcock or valve becomes seized, apply a little penetrating oil to the spindle where it meets the gland nut and allow this to work its way in. This should ease the fitting. If not, apply a little heat and that should release it. Don't be tempted to apply too much pressure as this may shear the spindle. If you can't budge it, then you'll need to switch off the supply to this pipework, drain it, and replace the valve.
Replacing the washer
Washers on stopcocks rarely need replacing as they are not often kept closed. However, if it does need replacing, the process is similar to that for tap washer replacement.
Repacking the gland on a stopcock
If water is leaking via the gland nut, this can be repacked to form a watertight seal.
Close the stopcock and loosen the gland nut with a spanner. Grip the body to prevent accidental turning of the whole assembly. Remove the gland nut from the spindle and, using a small knife or screwdriver, remove the old packing from the base.
Replace it with specially made packing or, if you are unable to find this, use a length of fibre string coated in petroleum jelly. Wind this into the base, packing it down tightly with an old screwdriver so that a good seal is formed.
Replace and tighten the gland nut before refitting the handle.