(The United Kingdom consists of England, Scotland, Northern Ireland and Wales. Though there are many other countries in the British Commonwealth (Canada and Australia, for example), they are not considered part of the UK.)
The UK really has to be split up for a discussion of scenery...
England has a few particularly nice bits in it, but it's mostly fairly flat and grassy. The Lake District in the northwest is probably the most famous of England's scenic areas, which explains why the youth hostels there cost £13, are booked all year round, and have huge tourbuses in their parking lots. I guess I'm a bit spoiled, being from Oregon (a very scenic state with high mountains, deep gorges, and a plethora of waterfalls and scenic desert landscapes), so I didn't find the the Lake District all that impressive. It's definitely pretty, but it didn't blow my socks off or anything.
Scotland is quite pretty, but reminded me a lot of home, so it didn't knock me out. Ben Nevis, the tallest mountain in the entire British Isles, is only about 4400' high, whereas Mt. Hood in my home state of Oregon is over 11,000', and is only one of an entire range (the Cascades), all of which are almost twice as high as Ben Nevis. Nevertheless, the Scottish Highlands are beautiful. Waterfalls are everywhere (of course, that's because it rains all the time), and the hills are covered in various colors of trees and flowers. I particularly recommend the town of Glencoe. I had no intention of going to Glencoe, but some friends in Edinburgh recommended it to me (many thanks to Ben, Mark and Keith!), and I was glad they did. I spent three days there, and it was absolutely lovely. It's a very popular base from which to go hiking, and I can certainly see why.
Northern Ireland has the Giant's Causeway and surrounds, which are lovely. The entire coast of Ireland is quite lovely, really, but as soon as you go inland, it gets incredibly dull. Rolling hills with lots of sheep. Yay.
I didn't spend much time in Wales, but it definitely surpassed my expectations. I spent a night up on Snowdon and a couple nights in Llangolen, and they were absolutely lovely. It reminded me of the Scottish Highlands. In fact, I have to say that I think the hills of northern Wales are even more beautiful. If the weather hadn't been the worst I have ever cycled through in my entire life (snow, sleet, hail, rain), I probably would have spent a lot more time taking pictures in Wales.
One thing the Brits have done fairly well is to preserve their old castles and other monuments. By the time I got to the UK, I was utterly sick of castles and cathedrals, but I did notice that everything is very well preserved. They even have their token Roman ruins (Hadrian's wall, which is quite possibly the silliest thing the Romans ever built, and the Roman baths of -- somebody really stretched their creativity naming this city -- Bath). Many of the most beautiful cathedrals are actually part of schools, such as the colleges of Cambridge and Oxford.
The cathedral in Bath is definitely worth a visit, and I hear the one in Durham is one of the most impressive in Britain, but it wasn't quite worth it to me to take a detour all the way up there just to see another cathedral. I didn't bother going to see the baths in Bath, but if you've never seen a Roman bath before, it's probably worth the outrageous entrance fee. The castle of Edinburgh and the Tower of London are worth a visit, but I thought Buckingham Palace was somewhat contrived. It felt like a Hollywood mock-up to me, and the entrance fee -- a whopping £9 -- meant it was something I would only do for the sake of saying I'd done it. Dozens of people told me that Stonehenge was a huge disappointment, and I'm glad they did. It's not the most spectacular thing I've ever seen, but my expectations were so low that I actually really enjoyed it, and I was glad I gave it a visit.
The UK occasionally gets some warm summers, but in general it's a fairly cold, rainy place. The entirety of the British Isles are pretty dismal as far as weather goes, and almost everybody who lives there will tell you the same. "If you wanted good weather, you came to the wrong place."
A word of caution: particularly in the mountains, the weather can change on a dime. Just because it's sunny doesn't mean you should go for a hike up in the Scottish Highlands without a jacket. People die every year on Ben Nevis doing just that, because it goes from sun to snow in minutes.
Britain was very cheap for me, but that's mainly because I spent so much of my time visiting friends whom I had met while in the mediterranean. The main form of entertainment is going to the pub and drinking a lot of beer, so A) it gets expensive very quickly (many Brits spend the equivalent of $30 on beer every night they go out) and B) if you're not a big drinker, you may get bored with it in a hurry. Going out for a real meal in a restaurant can be outrageously expensive ($30+/person), but you can get British fast food (fish & chips or the like) for about $3-4. Youth hostels usually run about £7-8 ($10-12). One thing to keep in mind in Britain is that many of the YHA/IHA hostels give a discount if you have a student card, but they DON'T TELL YOU, you have to ask.
Special note for expenses in the UK: London is expensive. Let me repeat: London is expensive. If you are flying straight into London, it is quite easy to spend all your money there and have nothing left to travel anywhere else on. You can go and see just about any play you could possibly want to see, but they're expensive. Most youth hostels in London cost about £15-18. Clubs have cover charges of £7-10. Seeing a movie may run £7-8. Ironically, the cheapest things in London are the things I consider best to see: the British Museum and the National Portrait Gallery. Both are free, but request a (voluntary) donation. I gave the museum £2 the first time I went, nothing the second time (you can't see it all in one day, or even three). With a student card, if you're willing to chance that you won't get a seat or that it will be a bad seat, you can often see plays at student prices, which are about £10.
Most people say British food is boring, but I actually like it. It is NOT good for you, however. It consists mostly of deep fried foods (fish, sausages, chicken, etc.) or other high-fat foods (bacon, sausages, burgers, eggs fried in fat, etc.). I find it quite tasty, but it gets pretty heavy on your stomach after a while.
Fortunately, it's possible to find ethnic food -- particularly Indian -- at a reasonable price just about anywhere in the UK. Take-out Indian food (to go out for Indian food they call "going for a curry") usually costs around £5 ($7.50), which is cheap by British standards.
The Brits have a reputation for being incredibly snobby and rude. I did find them to be incredibly proud people, but not rude. I actually found them quite polite and friendly. The fact that the English (not so much the Scots, Welsh or Northern Irish) consider their country the best in the world isn't really all that out of the ordinary. Americans are world-famous (or infamous) for saying that everything American is "the best in the world." Perhaps we get it from the English.
On the whole, though, I found people all over the UK to be very friendly and hospitable, sometimes to the point of being annoying. If you ask directions, prepare to get an entire speech on how to get where you're going. If, by the time they're done, you can't remember whether to turn right or left when you walk out the door, you can ask, but be prepared: they'll probably repeat the entire spiel for you.
In general, the Brits are pretty clean. One thing they do NOT seem to share in common with Americans is the need to take a bath or shower every day. Americans treat a shower as a treasured experience, Brits treat it like a chore. As a result, showers are not always very pleasant.
England is pretty flat. Scotland is reasonably hilly, as is Wales. Northern Ireland is pretty flat. There's nothing over 4400' (give or take a few feet on Ben Nevis, of which I don't know the PRECISE height), which should give you some idea.
Roads in the UK are generally well paved, but have very narrow shoulders, if they have any shoulder at all. You can't cycle on the motorways ("M" roads), but you can cycle anywhere else, even if it seems like it's a big, fast road. (Some of the "A" roads are quite large and fast, but you can still cycle them.) Drivers generally give you plenty of room, but having said that, I damn near got hit by a bus just today, which came literally within inches of me as it passed at high speed. The pavement is not always of very good quality, and is sometimes quite rough. Potholes are not usually a problem, it's just that the pavement itself is very coarse. Sometimes the older pavement on the shoulder is actually smoother, but watch out for glass.