Pre-1960? No.
Ipanemanian? No.
Anne Bancroft? No.

Let me summarise/recapitulate and answer Rosie's question as I do so.

You are looking for a song, written since 1960. performed by a popular* beat combo. The title of the song includes (or perhaps is) the name of a female fictional person. The song also has a connection to a real person (actually, many real people, but only one is of interest); to clarify my earlier response to INJ, the real person shares a name with the fictional person named in the song.

Now here is some more information for free: Wikipedia informed/reminded me that there are actually quite a few songs with the same or related titles. Some of these songs are better known than the one I have in mind (which is, remember, sufficiently obscure that it is not mentioned in Wikipedia). Of course, finding one of these other songs would be a possible route to the answer. The song that I have in mind is British. The song that I have in mind also has a tangential connection to a particular LU station. A fictional location is named in the song, but I don't think that's helpful.

You are not likely to guess it outright (although that's not impossible). Your best route might be to focus on the real person at this point. Or, if you like, on the LU link. You are also welcome to ask questions about the other songs that share the same title, but I warn you that most of them are not songs that I know.

*It's fair to say it was popular at the time. It's also fair to say it is largely forgotten now, I think.