@Jamie I think a budget of £100 - £150 will get you a stellar pair of headphones
I personally also favour the KRK KNS 8400
However, I would also be very happy with the AKGs Rich has mentioned - as well as the various versions of the Beyerdynamic
My general recommendation would be to make sure you go for a set of “round the ear” headphones and NOT “on the ear” headphones. This will give you MUCH better sound isolation and IMHO are MUCH more comfortable
The other decision to make is whether to for “open back” or “closed back”
If you are looking for a set of cans for recording AND mixing then I would say go for closed back - these will stop sound leaking in to your mic when singing and listening to the backing track
It will also keep outside noise to a minimum when trying to focus on a mix
If you are just mixing and have a really quiet environment, then open back headphones will give a slightly better sound as they minimise the internal reflections of sound bouncing off the the plastic backs - but in reality this is very minimal and (IMHO) probably not worth worrying too much about
I would also recommend checking the availability of spares - you can then go for a more expensive set knowing they can be easily repaired
I recently fixed my pair of Beyerdynamics and after some soldering, new ear pads and new headband cushion they are literally as good as new after about 10years!
Final consideration- do a bit of googling about the Ohm rating of your cans to make sure they match what you intend to plug them in to - perhaps give a store like Anderson’s a call to discuss
Other than that - good luck with the hunt and I think you will be VERY pleased with the improvement a good set of cans will make (and NEVER underestimate the importance of comfort! The KRK ones are so light and comfy they can easily be worn for many many hours!)