Are you trying to remove the stem or the headset? The stem, you'll need either a 4mm or 5mm allen wrench (is that what they call it in the UK? Not sure)
The headset, the top part comes off and the piece inside the frame, you'll need a headset cup remover (or a big ***** long screwdriver and a hammer)
Then a 4- or 5-mm allen wrench, and maybe a 6-mm to take off the top cap. You have a threadless headset- you remove the top cap, loosen the clamp bolts, then the stem slides off the steer tube. unstack all the stuff until you get to the top bearing ring, remembering the order, then you can slide the steerer tube out of the head tube to expose the lower bearing ring.
Have fun. Keep it all clean, and use plenty of new grease.
What type of headset is this or type of HB?
It looks like an Integrated headset. Could be zero stack but black on black is hard to pick out what it really is
If it's a stock headset on a production bike, knowing the make/model/year may help determine the headset details at bikepedia.com
1980ish Free Spirit Sunbird fixed * 1996 Mongoose IBOC Zero-G * 1997 KHS Comp * 1990-ish Scapin * Olde Western Auto Cruiser.
You may have sealed bearings in the headset.
Bikes use brakes to stop.
If your bike has breaks, don't ride it.