Have you decided anything yet ?
When I had no phone line at home for a time in 2006/7 (and therefore internet access was awkward, especially as some of the time I remote control clients' PCs to iron out problems), I worked from the under-the-stairs cupboard at a friend's shop, using my laptop and his internet (and there was a drinks machine in his workshop, the next room, so plenty of choices of refreshment, and it even used my favourite, Kenco coffee!).
I have a number of (Toshiba) laptops, a Dell Inspiron and an Acer, plus a pile of desktop and iMac systems) with the vast majority bought on Ebay for 200 pounds or less.
While they were suitable for me (s/h running XP and then a few running Windows 7), I'd expect you to be getting something in the 300-500 pound price bracket, with either Windows 7 (if you can still find it, and I know I'd probably prefer it even now) or Windows 8.
There really are a lot to choose from and someone not many weeks ago listed 4 laptops running from 299 to about 349. I'd probably recommend buying from say John Lewis (2 year warranty, price match) but trying beforehand in PC World, say, as they have a wide range, and perhaps a big Tesco store if they have a dedicated section with laptops/PC on display.
A laptop would probably be advantageous just for the ability to take it with you to a client's site, if absolutely necessary, so do think about weight as well as battery life. However, I'd go with one of the suggestions about having other things to plug in (such as a USB keyboard, and possibly a screen, too), so you can sit at a desk and have a screen closer to eye level, and a full size keyboard. Recent laptops have sometimes 'skimped' on USB ports, so consider a powered USB hub (so you can plug in any extras - eg external hard drive - 1 TB {1000 GB} is down to perhaps 60 pounds, plus your camera, mobile, iPod {well, you may as well expect to have some new toys from your new business...} but as well as having a powered hub you could get a couple of the cheap, unpowered hubs {and 1 metre USB extension cables} from Poundland for the day when/if the powered hub might die. Best to have considered the eventuality and been prepared.
Similarly, when you have 300 quid to spare, get a spare laptop of similar spec and what's more, use it too. If this is your business then it's not too much to consider and if your laptop was being repaired under warranty and away for 2 weeks, your clients would be less than impressed if there was no chance of anything being worked on...