Personally, i'd go for a desktop. More bang for your, erm, pound. If you're concerned about size, you can always get a PC based around the Shuttle systems, or a case like I use at work:
Which is a nice lickle thing
As for laptops, generally I'd recommend sticking with Dell, Toshiba or HP. If you're editing, get loads 'n' loads of hard drive space, which, for £1600, you should be able to afford plenty. One thing to watch out for though is, apparently for video encoding, the Pentium 4 M is a lot, lot slower than the desktop version, so if you are getting a laptop, get one with a built in P4 desktop processor. Or, if you're buying HP, I think they do Athlon64 based notebooks, though I may be wrong.