Annie:
It appears to me that US copyright law is very similar if not the same as international (and UK) copyright law. Whether or not the trademark laws are also the same, I have to admit I don't know. I can say, though, that trademark and copyright are two different things and you *can not* copyright a character name (or situation). You can only copyright an individual "thing" in a certain form. Although there are some protections regarding derivative works...
In the UK, I believe by simply using a name in a given sphere, one acquires a degree of rights to it within that sphere. So, for example, if I chose to trade as a medical writing company called, say, Viragene, hacked up an appropriate website, printed a few flash business cards, and generally said 'hello, my company name is Viragene', I would acquire rights to the name such that someone else trying to use it within the medical writing sphere in the UK would be infringing my prior use rights. I wouldn't even need to register the company, let alone bother trademarking Viragene.
It would seem to me that the BBC et al. might therefore be considered under English law to have acquired prior use on say Avon -- when used in the field of 'cynical black-leather-wearing computer genius with a talent for sarcastic one-liners in sf media'. English law would I guess hold because the series was created in England.
I think trademark/branding laws differ substantially from country to country. Copyright, as you point out, is entirely different and these days slightly more internationally standardised.
...and that's where you get into the whole profit/non-profit, commercial/non-commercial, etc. debate of fan fiction as a whole. Generally, my personal opinion is that fan fiction, fanzines and fan art qualify for fair use.
Obviously, morally speaking, I agree with this, otherwise I wouldn't have produced one. However, I'm not convinced that we are truly legally in the right, merely too small for anyone to bother with. If a fanzine made substantial profit, then the legal side of things might start to have more meaning.
Tavia