need for suggestion

Buy a new pair of iPhone headphones from the apple store. You already know that the sound quality is good/ same as the other ones. Think they cost approx £26

 

The first suggestion will be not to even consider the previous answer. The second will be to go to your local hifi store (or any other place you know that sells headphones/earphones/whatnot and try out the ones that you think are in an acceptable price level until you find a pair that you like.

I have no problem using the included Apple earphones, but considering the bad fit and poor sound I would never pay more than a few dollars at the most for them.

 

Almost all headphones/earbuds/IEM's will sound better than the ones provided by Apple. If you go to a good store you can listen to a bunch and pick the one you like best, alternatively, buy a pair from a box store and return them if you don't like them.

If you want people to give you actual suggestions, we need your budget and type of headphones that you want (over the ear, on the ear, earbuds, in ear monitors, etc.), type of music you listen to can also be helpful.

If you want to research yourself, browse around headfi.org

Good luck.