I agree 100% with Alex don't go for cheap as they will not be that good for long term listening.
I have owned many an amp from Creek, Musical Fidelity, Project, Sugden, Graham Slee right up to the mighty m902 Grace Headphone amp.
Ok first thing at your budget you need to push it up to about £75 minimum (£100 best as a starter) and then you need to look at the second hand market ebay, hififorsale.com, loot.com, bargain pages, etc. At that price you are looking at the Project Headbox, Creek OBH 11 (older model that the current 21 series now built on) and maybe the Musical Fidelity X2 (can upgrade the tubes for improved sound). Like the host said you will need headphones of probably equal cost to match and get some reasonable cable say QED quinex 1 minimum (about £10 second hand).
Once again if you go down the second hand route (this can be better if the can's in good condition as they are already burnt in). You will be able to get some good can's the one's to go for are Sennheiser HD 590, HD600, Grado 60, 80 (and maybe even 125) these will set you back between £60 and £100 if you look around so the total investment would be around £150 to £200. Wow!!!!! you will say but trust me nothing will prepare you for what you will hear when you start off with this setup. You will think man my ears are fantastic. Also to get the same sound from an amp, speaker combo you got to be looking at near £1000 really. I started off a few years back down this route and now have ended up with the Grado RS1 and Grace amp these combined are worth in excess of £2000 and I'm so happy with them. (I do use for work too so I have an excuse). I used to be really sceptical about all this 'high end' stuff preferring the stuff I got from Dixon's and Curry's but once I stepped into the light you can't believe the difference. All my friends have now been 'converted' too. If you live anywhere near Telford let me know and you can come listen to your own music through some of these amps and you'll see for yourself.
The one downside is once you start you want more (and there is more out there). If you do take my advice please let me know what the result was.

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