There’s nothing in the law that says you are not allowed to wear headphones while driving in the UK, but if you drive on the continent there are countries, like France, which do not permit you to drive with headphones. Illinois in the USA has a similar law.
Just because you are allowed to doesn’t mean it’s a good idea. The main risk when driving with headphones is the distraction. Police are within their powers to stop and fine you if they believe you are driving while distracted and this doesn’t just include wearing headphones, it could include eating, drinking, putting makeup on and more.
Headphones mask the sound of other road users (e.g. ambulances, fire engines, etc) meaning that you might inadvertently block them by not giving way. When manoeuvring, being able to hear the engine is an advantage, especially if you drive a car with a manual gearbox. Another road user might use their horn to warn you of a danger and you might not hear that.
Being able to hear what your car is doing also enables you to pick up on any unusual sounds that might start but be quiet at first. One example is when you get a nail in your tyre that causes a slow puncture. At first, you might detect a very slight throbbing in the noise coming from one of the tyres and you won’t hear this if you have music on. CV joints start making a noise when turning when they are wearing out.
If you are in an accident and your headphones are deemed to have been a contributing factor you might be charged with careless driving, or driving without due care and attention.
If your headphones are connected to your phone or another device like an iPod it is illegal for you to operate it while driving. A study found that listening to your own choice of music increases your accident risk when driving, whether on headphones or through the speakers.