There are at least 2 dozen UK native species capable of piercing human skin. Basically, bigger spiders have bigger fangs, so are more likely to be able to bite. This says nothing about the likelihood of them doing so though. No UK spider species are aggressive, and any bites result from the spider being trapped, either in clothing or by being handled. Your point about handling lots and not being bitten is very much to the point. They just won't bite, unless given no choice.
Bites can be painful, but unless you are unlucky and have an allergic reaction to the venom, no UK species is in any way dangerous to human health. The Steatoda nobilis that I linked to above is probably about the worst, and even then a bad bite would result in an inflamed and painful skin lump and possibly a raised temperature.
The risk (and pain level) from something like a wasp sting and anaphylactic shock is much more severe.