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.

Taking the suggested route

Song from the sixties? Yes.
Real person still alive? Yes.

(Oh, and two other LU stations are tangentially linked to the LU station that is tangentially linked to the song.)

Referred to by given name? Yes.
Caroline? No.
Beatles? No. I remind you that I said that this particular group is largely forgotten.

as in 'Eleanor Rigby' or 'Jennifer Eccles'

[INJ, Projoy] The song title consists of a given name (which might or might not be a nickname) and nothing else.

Lola? No. (I really do think it is unlikely you will just guess it)

Real person an adult? Good question. I'm almost certain that the answer is yes.

British? Yes.

Great beauty? *audience laughter* Whether the person was a great beauty I have no idea. I'm confident that the person was not widely renowned for the fact.

Real person known mainly for profession? No. (But the fictional person, perhaps yes.)
Real person known simply by first/given name? The least misleading answer is Yes, though the strict answer is probably No.

Real person famous for relationship? No. Check your assumptions.

So (trying to summarise it for myself). The answer is a song title from the sixties released by a group who are not particularly well-known now (I'm thinking of the stature of The Honeycombs). The title is a woman's given name/nickname . That name is also the name of a real individual also identifiable solely by that single given name (or perhaps more likely, nickname). The real individual is still alive and was probably? an adult when the song was released.

Real person the same for every questioner? Yes. But if you had asked the question a bit differently I might have had to give a very different answer.

And I think your summary is accurate. Don't think I know/remember the Honeycombs (but then I had forgotten the name of the band that sang the answer before I looked it up, even though I remembered several of their songs).

Was the real person famous? No. *applause* Now question your other assumptions. :-)

Having googled The Honeycombs, I think INJ has it about right. The group that sang the answer is perhaps a bit better known (although its Wikipedia entry is shorter), but certainly roughly equivalent in stature.

Speaking of The Honeycombs, the first second of this video is worth seeing.

Like 'Grandma'

BTW - Can't look at Youtube from work. This is getting to be more and more of a restriction.

Real person identified by relationship? No.
Non-famous real person female? No! *applause*
(I'm reasonably confident, by the way, that INJ will know/remember the answer, and I think most Morniversers of my age or older will also know it. I'm less sure about Young Master Projoy and his contemporaries -- they may need to use the google -- although I think there is a good chance that he (they) would at least know another song by the group.)