I assume you live in the UK, if not buy your bike in your own country -it will give you time to get things sorted out. Plus if you fly in, some airlines don't charge you internationally for bikes. And unless you have the tools and expertise to build a bike or a friend who does and will do it for you -don't. Really, the cost of building a bike is not cheap unless you have the parts and tools already or that friend, usually it's much better to buy a bike.

If you are in the UK, you're actually lucky, the UK has far more quality touring options than over here in the USA. Dawes Galaxys would be good choice -I'd think if you could get one for cheap money (e.g. ebay). Another thing to consider is getting an older mountain bike and putting on slicks -the older mtbs have almost tour-like geometry as well as rigid front forks, good tyre clearance and rack mounts. If I was on a budget, my first choice would be any bargain tour specific quality bike (that fits!!!) that I could find, followed by any bargain old mtb (that fits!!!) I could find. Buying the mtb would mean you might want to put money aside for new tyres and tubes, and possibly fenders (mudguards).

One down side to the UK is that craigslist hasn't quite caught on over there -over here in the states on craigslist its really not hard to get an old quality mtb for less than 50 quid -I really do see them all the time.

So... to answer your question, and based on what I've seen and had opportunity to buy if I wanted to, I'd say 50 -80 quid. Course, the problem here is that's what *I've* seen and had opportunity to buy over here in the States. And I didn't figure in panniers either (and are you going to camp? What about a tent? Sleeping bag? etc.) Your cost could vary so much based on just finding one item at a really bargain price.

Best thing if you have it: patience and a watchful eye for the best deals. Good luck!