Hi Morgan,
One thing to keep in mind with thin guitars is that they are not going to produce much sound when played acoustic. They'll produce more than an unplugged electric, but they will still seem pretty quiet by acoustic standards. So, while you can play them without an amp, they're really designed to perform best when plugged in.
A bunch of companies make these guitars in varying price ranges:
-Alvarez has their "Fusion Series" (http://www.alvarezguitars.com/prod_byseries.php?SeriesID=2) which aren't bad.
-Dean has some thin body acoustics, but their acoustic guitars are generally pretty awful so I wouldn't recommend them.
-Epiphone -
-PR5-E (http://www.epiphone.com/news.asp?NewsID=1564) which has a thinner body. It does have a laminate spruce top which is not something I would recommend if you're just going to be playing acoustic, but if you're plugging in and playing through an amp, a solid top isn't as vital, though it's still much preferred.
-Performer ME (http://www.epiphone.com/news.asp?NewsID=729) which is also a laminate top. It's a thinner than normal body for an acoustic, but not very thin in comparison to some others. If you want to hear it, here's a review of it (http://www.acousticguitar.com/article/default.aspx?articleid=23634)
Fender - They have the Stratacoustic and Telecoustic (http://www.fender.com/products/search.php?partno=0967300006), (http://www.fender.com/products/search.php?partno=0967310006) designed to look like acoustic versions of the Stratocaster and Telecaster, but neither of these acoustics are all that good.
Godin - Their A6 (http://www.godinguitars.com/godina6ultrap.htm) is pretty cool, but you'll definitely need to plug in to an amp if you want to get real sound out of this one.
Ibanez - They've got a few different ones. Their AEF series is billed as a thinner acoustic-electric, but with a 4.25" depth, it's not that thin. Their Talman series is even thinner at 3.25" inches (http://www.ibanez.com/AcousticGuitars/Series-talman)
All of those should be within your price range. But another option that you may want to consider, if your main focus is portability, is to go with a travel guitar. Pretty much every guitar company makes one, and some are better than others. Ones I'd recommend in your price range are the Little Martin, Baby Taylor, Art & Lutherie Ami. Other good, less-traditional options are the Voyage-Air (folding guitar) or the carbon fiber travel guitar made by Emerald Guitars (which is based in Ireland). A huge advantage of carbon fiber guitars is that they're pretty indestructible. Sand, heat, cold, water, etc. won't faze it at all, though all those elements will damage a wood guitar. Since you're in the UK, this would be a good site for you to check out for the last two I mentioned (http://www.playawayguitars.com)
In my opinion, I'd go the travel guitar route rather than looking for a thin-body acoustic. They're more portable and, in my opinion, tend to sound better when played acoustically than a thin-body guitar does.
I hope that helps. Good luck!
Anyway, hope that helps.