PS: If you use Bluetooth headphones, the headphone socket on your set won't be involved at all because the Bluetooth transmitter is built into the set itself.
However if you did want to go down the alternative route of plugging a transmitter unit into the socket and then having a matching pair of headphones, these are superb. (I use them myself):
https://www.argos.co.uk/product/2473666
As you've got Bluetooth available to you though, it would probably make far more sense just to stick with that way of doing things. You can buy Bluetooth headphones in loads of places (such as supermarkets and discount stores) but for some really good ones, which are really comfortable and with a long battery life, I suggest these:
https://www.argos.co.uk/product/7143726