I would like to purchase a pair of headphones for under £100 (GBP) preferably about £50. I've done a little research and decided I would like some on-ear or over-ear, closed back, noise cancelling headphones. I am not too worried about if they fold away despite being "travel" headphones. I'll probably use them when I'm walking and on the train, or studying in public, so I don't want them to leak sound. I appreciate the budget may be a little low for noise cancelling, I am willing to drop that feature if required to maintain the budget and sound quality.
You should consider buying IEMs instead on such a tight budget. Something like the shure se215. I own the slightly higher end se315 which do a really really nice job at isolating, especially with the foam or the tri flange tips.
a review: http://www.youtube.com/watch?v=y_oBJX1rNCQ
+1 for the iem thing. For that price range, if you want portable and isolating, iems are the way to go, for sure. However, I would suggest looking at Etymotic's iems instead of Shure's. The HF5 have a better overall sound than the SE215 (unless you prefer a warm sound to an accurate one, in which case the SE215 are the way to go), and have noticeably better isolation.
Below is a multi-review by one of the most well respected men in the game. He has the SE215 and the HF5 on there, if you would like to compare them. There are plenty of other reviews available online as well.
IEM's are probably the way to go for what you describe. I have a pair of Sennheiser CX 495s that are decent. Definitely block out sound. The IEMS the guys suggested above likely have a better sound stage though. My other travel headphones are Harman Kardon CL Precisions. They are on ear, but still do a decent job of sound isolation. Sound is pretty good when paired with a small portable amp as well. They also fold flat and come with a leather case, which is nice. MSRP is around $250 (£160), but routinely sell for around $100 (£64) and often go on sale for $40-$50 (£25-£32). So that's something to consider (though, not sure about UK availability).
Since you say portability isn't that important, there are plenty of over ear cans in that price range that will likely deliver better sound than anything posted here so far. Audio-Technica ATH-M50 for example, or the ATH-PRO700 if you like a little more bass. The ATH-PRO700 is also on sale at buydig right now too: