Is the valve fitted in a plug screwed int the radiator(usually about 1/2" or 3/4" diameter with a hexagon head surrounding the bleed valve)?
If it is, then you may be able to remove the plug complete with bleed valve, and replace the whole assembly with a new one.
Turn your heating off, and let it cool down. If anything does go wrong, it's bad enough working with cold water running up your sleeve, You definitely don't want scalding hot water.
Shut both the lockshield and wheelhead/thermostatic valve feeding the radiator (note how far you have to turn the lockshield to close it).
Expect some air and water to come out when you loosen the plug.
Wait for the air and water to stop before fully unscrewing it. If the flow doesn't stop, the valves aren't sealing. Either re-tighten the plug and consider other options, maybe draining the entire system, or get ready to work VERY quickly and get VERY wet
Water from central heating systems is almost guaranteed to indelibly stain carpets, clothing, wallpaper and paintwork, so have buckets and old towels ready to catch it. A dustpan is useful as you can put the flat edge against a wall to catch drips.
Don't rely on a thermostatic valve to remain sealed for long- they open themselves as the room cools.
Prepare your new valve ready to screw straight in before you start. Collect everything you think you could possibly need and place it directly to hand. It's no good leaving your bucket in the garage until you have water running down the walls - even worse if it's still on the shelf at B&Q.
If the valve screws directly into the radiator, I would consider :-
1. packing out the flats on a radiator key with strips of metal cut from a old tin (aluminium foil is too soft) so it's a drive on fit on the valve.
2. Glueing a key onto the bleed valve, using something like Devcon 'Plastic Steel' or an epoxy resin.
3. Cutting a screwdriver slot in the top of the bleed valve with a small dremel cutting disc or the end of a junior hacksaw blade.
4. Finding a small 1/4" drive socket that can be driven over the remains of the screw to grip it.
5.Flattening a bleed valve key to grip what's left of the bleed screw.
Any way round it, you will probably want to get a new bleed screw first.