Firstly, all "serious" British crosswords are "Cryptic" ie once you figure out what the answer is, it's apparent why that's the correct clue, but figuring out the answer from the clue involves lateral thinking and some skills learned from years of staring at such clues.
e.g. Private Eye's crossword 726 (back in April), clue 23 down,
"He finally gets to penetrate agreeable person (relatively) (5)"
The correct answer is "Niece". "Nice" can mean agreeable, the final letter of "He" is E, and so by having the letter E "penetrate" the word nice you produce "niece", a person who is a relative.
[ and yes, Private Eye is a satirical magazine, the crossword clues are, likewise, intended to make you a little uncomfortable while you laugh ]
Secondly, British crosswords are arranged with black "dead" squares between letters to produce more of a lattice, in which many letters only take part in one word, as a result longer answers are common
e.g. same crossword, clue 26 across is
"Figure on getting your teeth into our statistical revelations (6,9)"
The answer was "Number Crunching".