I always sent a thank you email after an interview in the US, reiterating why I was right for the job and addressing anything that I thought maybe I didn't do as clearly in the interview as I would have liked. Not long, but I did do it.
In the UK, I've only worked with recruiters so I leave them to do the feedback bit and let them know if I'm interested and want them to reiterate my fit for the role. Which has worked well.
If you are not working with a recruiter and are communicating directly with HR, I do think that a short note afterwards to HR (or the hiring manager, it's likely they'll give you their business card) is appropriate. However, it's not expected.
ksand, I think what Jimbo means is during the interview "asking for the job." I always do this (if it's a job I've determined I want). It's basically saying at the end of the interview, "Have I told you enough to convince you I'm a good fit for this role?" "Will you be recommending that I advance to the next stage?" It is rather bold, but I've always done it in a polite, honest way. It gives you the opportunity to address any concerns the interviewer may have right there. And I also think it shows people that I have balls.
But for Moogrit, it is VERY appropriate to ask for feedback after the interview from your HR contact or recruiter. If you don't get the job, it'll give you a bit of insight you can use for your next opportunity. Good luck! Let us know how you get on.