I highly recommend the Koss BT540i. They can be had for about $200, which is just within your budget calculated via Google Pounds to Dollar converter.
http/www.ebay.co.uk/itm/Koss-BT540i-Wireless-Bluetooth-Headphones-/381732663868?hash=item58e10a323c:g:QGkAAOSwU-pXrEjX
I've used them for almost two years now and I couldn't be more impressed with them. They're Bluetooth, but you can hard wire them to conserve internal battery or to use them for devices without Bluetooth capability.
At first they sounded kind of tinny, but I read somewhere that large headsets have a break-in period. I just set my phone to shuffle all of my music and let it play overnight. When I woke up and tried them out again, the bass was crisp and well defined yet not overwhelming, the vocals were well defined and easy to follow even on songs with multiple lead guitars, and the highs were very crisp yet not distorted at all. I am very impressed with this model. I think the only downside to them is the fact that they sweat to my head if I wear them outside on a hot day, but I think this would happen with just about any over-the-ear headset.