That won't work as the centre part of that tap connector would have to fit inside the plastic fitting and i don't think it will. A few fibre washers inside your female fitting and ptfe tape or jointing paste will probably sort it.
If you are talking about connecting to iso valves then buy a flat top valve.You could also add a fibre washer into the nut if you are worried about the rubber washer.
The thread will be BSP. Drill it out and then tap it with a 1/4 inch BSP tap.You can then screw in a 1/4 inch brass nipple and a female cap.The cap could then be used to bleed the rad.
You can replace the whole cartridge,if you know which one it is.There are a lot of different types.
Or you can just replace the ceramic disc for a couple of ££'s.
Do you know the model of tap ?
If that has snapped off inside the tap then you might need a new tap ?
If it is not snapped then you can replace both hot and cold heads for less than £15.
Look at bath tap replacement heads online.