Is there a small hole or small round rubber on the chrome below the handle? If not have you tried to just pull the top up More on reddit.com

You just need to fit a new cartridge. Please don't replace the whole tap because a small replaceable part is broken. What you need to do is turn off the water to that tap. Take the top off - there will probably be a grub screw around the back or something like that holding the top on. Under there will be a large nut that locks the cartridge in place. Undo the nut and find a replacement cartridge online, you'll need to measure it accurately to get a replacement. Have a look down the tap body at the cartridge seat (where the cartridge seals against the body of the tap). I wouldn't be surprised if you saw some scale build up considering how your tap is leaking. A bit of vinegar in there will sort out the scale, you want the seat to be nice and clean. Drop the new cartridge in place, fit the bolt, put the top back on and you're good to go. Cartridges can be quite expensive at some places but shop around and you'll almost certainly find a good deal. I've got a tape with an unusual cartridge design and I ended up buying new ones direct from China. I got them for £1.50 and they are holding up just fine - took forever to get here though. More on reddit.com