I think your budget may be a bit low. I've been looking at getting a new laptop recently and my budget starts at £400
IMHO, you want a fastish processor, Intel i5 or i7, or a multi core AMD processor. i7s are normally mid to top of ranges. At least 8Gb of RAM, though more is better if you plan to do anything complex. Most budget laptops come with 4Gb and a large part of that is used by the Operating System. Photoshop works better with more RAM, though some say you don't need more than 16Gb. A Solid State Drive instead of a normal Hard Drive would be nice and quick, but probably out of your budget. A good quality screen should be a high on the list too if image editing is the computers main use. I've seen a lot of people saying get an IPS screen for the quality, but again they cost. (And if I'm waffling BS here somebody please chime in)
Saying all that, I currently have a 5 year old HP Compaq with AMD Dual Core 2.10Ghz processor, 4GB of RAM and a 320Gb slow HD, and opening an image editing with Camera Raw and save an image it is fine. Start opening a large folder in Adobe Bridge, where the program may have to build thumbnails previews, make Panoramic images or large multi layered Photoshop files and the thing struggles. Have any other programs open at the same time and things really starts to slow down. I sometimes have to have a number of different programs open during a demonstration, but most people wouldn't.
Hopefully someone more up to date and knowledgeable will post some help.