There's a slight problem with your list: most good board games cost more than £25. If you've got the budget to go up to £40, the amount of possibilities expand tremendously.
The only games I know of that would fill
every of those criteria would be
Guillotine or
Fluxx, as both are quite a bit cheaper than most other board games I know of, and the game box will easily fit in your pockets. They're still pretty damn fun, mind, especially
Guillotine. If your budget can't handle more than what you mentioned, get that. You're guaranteed to get some fun out of it.
Still, if you slightly raise the price point, you're bound to get more out of it. For the aforementioned £40, you can get your hands on the following gems:
Ticket to Ride
Hands down the best family board game in existence. It's incredibly simple to get into, plays fast and interestingly, and at the same time has a lot of strategic depth. If you're only ever going to buy one board game, this one is it. It's not my personal favorite board game (those would be 7 Wonders and BSG), but it's an incredibly good buy because it's a game almost anyone will enjoy for years.
Settlers of Catan
Almost everything I wrote about Ticket to Ride also applies to this. It obviously plays differently, but at the core it's got the same appealing features as TtR: it's accessible, the turns are fast, and it has a good amount of depth to it. I remember a Cracked.com-article referring to this game as the "the binary test for 'Have you actually played board games, or just terrible family ones?'", and it's pretty much that. Highly recommended.
Carcasonne
This game is one of the most replayable I know of, simply because building the game board from scratch is the entire game. It's thoroughly enjoyable if you're playing this with the right people. It's, however, quite rage-inducing if you're playing it with the wrong people. There's few things in the world that are more enjoyable than finishing a mega-city, and there are few things that make me as angry as having a twat ruin said city(or worse: steal the credit for it). Still, ruining/stealing cities and fields from others is fun, so it definitely get a thumbs up from me.
..I'm a horrible person
Dominion
It's a card game about using your cards to buy more cards from a selected set of card piles, in order to buy even more cards from said piles. Very fun, and very varied, but not quite as fun with only two people as it is with 3 or 4.
Munchkin
It's a silly parody of tabletop RPGs that's great fun in more than one way. It's about backstabbing, being a jerk to the other players, and getting loads of treasure. And having fun while doing so. There are a load of different versions out, but the difference between the versions is usually what kind of setting they're making fun of.
As a note: I've played a couple of other games from the same company,
Chez Geek and
Ninja Burger. They're fairly similar and also quite fun, but I definitely prefer
Munchkin to them.
I'm also going to throw in a couple of games that require at least 3 players in this list, because they're bloody great and deserve a mention.
7 Wonders
It's basically "TCG-drafting: The Board Game", which makes for some damn compelling play. It's one of my personal favorites, and while you'll need 10 minutes to learn the rules before you can start, the game plays fast and has a lot of mindgames and other interesting stuff. It's also very well balanced and has a multitude of effective strategies, giving everyone a chance while usually allowing the better player to win. I cannot recommend this game enough.
Cards Against Humanity
Also a cheap alternative, and one of the best party games I can think of. Provided you and your friends don't mind the game being about setting up jokes about racism, holocaust, teen pregnancy and dead hookers, to name a few of the things in the game. If you can handle that, this is one game you don't want to miss out on.
Battlestar Galactica: The Board Game
Just to throw that out there: this thing doesn't even match any of the points on your list. It's got quite a few rules, takes up a lot of space, needs at least 3 players(5 or 6 is preferred) and a session usually lasts 2-4 hours. So know that I'm only mentioning this because it's
a fucking masterpiece. It's incredibly tense, as the entire premise of the game is that you don't know if the guy sitting next to you is trustworthy or wants to kill everyone, and the game mechanics are otherwise incredibly solid and balanced. If this sounds at all interesting, and you have 3-4 friends that could be interested in giving this a go, I'd say go for it.
And, as a final closing note: even though you're seemingly not interested in chess, it's the most economical alternative as it can be played through sites like chess.com [http://www.chess.com], and there's a great amount of helping material out there to get started at playing. I recommend giving this a shot as well, considering it's actually free. =)
And, yes, I love board games =3