That's a thermostat. Technically it controls the boiler, not the radiators. It makes a difference as you can also get little controllers for each radiator that work together to turn on the heating just for a particular radiator.
You can replace it with a new thermostat, but there's a lot of choices around depending on what your boiler is, what your budget is and what you want to get out of it.
For example, that's a Worcester thermostat, which means you've probably got a Worcester boiler. That means the Worcester Easycontrol is probably compatible (you should check before buying).
Or you could go for a Hive or a Nest, or probably a dozen others depending on what features you want. So, what do you want?