Your central heating system has nothing to do with the feeds to your kitchen taps. If there are no valves on the feeds to the taps, we'll need a bit more info before we can help you.
Do you have a hot water cylinder? Or is the water heated instantly by your boiler?
To turn off the cold, just turn off the stopcock, then open the kitchen tap to let the pressure out. There will still be a bit of water in the pipes, which you can catch in an ice cream tub when you cut in. The hot side depends on whether you have a cylinder or not, but as you're in a flat i'll run on the basis that you don't for now. If you don't have a cylinder you'll be on a combi boiler, and switching the stopcock off will have also shut off the hot water, so you can repeat the process you used for the cold side. If you do have a cylinder it's slightly more involved, but only a little bit.
Once you've depressurised and cut the pipes, I'd suggest putting a couple of isolation valves on the pipework, that way you can switch the water back on to the rest of the flat and carry on working on your sink.