How serious an insult is "wanker" in British English? [NSFW]
Solution 1:
It's probably worth prefixing all this with the caveat that, as discovered from the discussion on your previous question, this does vary quite a bit between from place to place (and possibly between classes, professions, sexes etc...), so do beware that what answers you get may well not apply to the whole of the UK :)
I'm not sure which films you've been watching, but the reaction you've observed may have more to do with the tone the words are used with: if you walk into a pub and call someone you don't know a cunt, you can be fairly certain of a fight. If you instead call them a wanker, your chances of getting away without a fight are better, but only slightly so. With either word, anyone being referred to with it is likely to get very angry.
That said, just saying the word wanker is much less shocking than saying cunt: in the place I work (which is admittedly rather tolerant of so-called "bad language"), people might often use the word to express their frustration with someone (though never anyone working there) — say, a persistent and rude telemarketer who won't leave them alone, or a particularly unhelpful customer service rep from the phone company. Or perhaps someone who cut them up on their drive to work. Use of the "c-word" is much more rare (that would be reserved for someone who had, say, driven into their car and written it off...). And it is telling that there is no corresponding expression "the w-word". (Well actually there are many possibilities — 1, 2, 3, 4, 5 — but none of them refer to "wanker"!)
Of course the dynamics of insults are very different between close friends, where much stronger language can be used, and indeed being incredibly rude can often be a mark of affection. Tone is everything, and I would never advise doing this unless you are totally sure what you are doing!
Solution 2:
It's not terribly insulting.
A quick aside into the derivation, for those watching from across the pond: "to wank" means "to masturbate". "Wanker" is an agent noun derived in the usual way. Used as an insult, which is pretty much the only way it's used normally, the implication is that you are lacking in the girlfriend or boyfriend department, and Mr Hand is about the only friend you can get in bed with you. It's essentially identical in meaning to "tosser".
Between friends, it's the sort of insult you would use if you're annoyed with someone. No great harm is done, and your irritation is effectively put across. You wouldn't use it in polite company, but it's by no means an unforgivable insult.
Between people who don't know each other well, it's a direct attack on someone's sexual desirability or prowess. That's the sort of thing that starts fights, especially when it's chanted as a taunt.