"She's the most incredible character to play, and certainly when the role was offered to me, I had obviously no idea of the journey that both she and I would be undertaking - because obviously in the very first Silence in the Library story, she dies," Kingston exclusively tells RadioTimes.com.
"So, I just thought it was a two-episode job. Little did I know! I also didn't really know the personalities of Russell [T Davies] or Steven Moffat, and if I had, maybe I would have had an inkling that there must be more than this."
River's had countless adventures since she was first introduced more than a decade ago - she's appeared on-screen with three different incarnations of the Doctor and, in her work with Big Finish, Kingston has collaborated with every single living actor to have played the Time Lord.
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But there's one particular scene that many fans will never forget. In the emotional season 6 episode A Good Man Goes to War, River reveals to Karen Gillan's Amy and Arthur Darvill's Rory that she's their daughter, Melody, providing a plot twist for the ages.
In an incredibly apt turn of events, showrunner Moffat told Kingston about the reveal a good six weeks before everyone else, with the actress having to keep the explosive secret to herself because... well, spoilers.
"On this particular occasion, I was asked whether I'd be available, and Steven also contacted me and basically gave me the rundown of the storyline ahead of anybody else knowing," she recalls.
"He didn't want [the other actors] to know, because I think he didn't want their performances in any way to be altered with that knowledge - and also, in a funny sort of way, in the episodes that we had filmed prior, I didn't know either.
"The performances that you get from all of the actors are incredibly true, because there is no knowledge about who you really are or what you're going to reveal.
"I quite liked that, because you literally play - and, in fact, one always has to do this with Steven because he has so many threads that he's just tossed out to drift on the wind, until he decides to pull that thread back in and tie it up with something else. So you just have to literally play the moment all the time and not think about anything else.
"So, when Steven did give me this insight, I had a very big secret that I had to keep. The other actors, Karen, Arthur and Matt, they knew that I had a secret and I just wasn't going to tell them.
"There were bribes and all sorts of things... but I wasn't going to give the secret away. Even on the filming day, the script didn't have the reveal in it.
"Steven didn't put it in the script because he didn't want any of the crew to know and he didn't want that storyline and that secret to somehow get out before the audience actually saw it for the first time on television.
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"I've got a feeling, and Steven might say I'm wrong and that I've made this up - but I've even got a feeling that the crew were given different sides, so that they literally did not know until the words were spoken in the scene, and it was only on that day I think, or maybe the night before, that Karen, Arthur and Matt got given the sides and they were let in on the secret.
"It was a really big deal, and in a funny sort of way, it did make it all the more emotional when we played it... I'm very good at keeping secrets!"
River's final appearance in the show came in The Husbands of River Song with Peter Capaldi's Twelfth Doctor - an episode Kingston classes as one of her favourites.
"That moment with Peter Capaldi, when I suddenly realise who he is, that, for me, was such a hard moment to film - because I knew, obviously, as Alex, but I had to not know as River Song who he was until he says, 'Hello, sweetie,' and that was very hard emotionally to stay innocent of the knowledge."
But she's been very open about her desire to return on-screen - and it certainly seems like it would be within the realms of possibility.
"Obviously, in terms of the Benjamin Button of it all, I am not getting younger! Even though the Doctor isn't getting any younger either, he looks it - whereas I don't! But I did actually think that River could always be called back through the internet.
"Because she's saved on a computer, she could hack into any computer in any system in the universe. She could become anything, she could be an avatar, she could be anything that you want her to be off a computer screen. I thought that would be a very interesting way to go with that character - if one wanted to..."
She adds: "I would have liked to have done some more flying through space! I really enjoyed it, I would have really loved to have been strapped up again and whizzed along a zip line from one end of the studio to another - I can always do a bit more of that!"
But, in the immediate future, we've got the return of David Tennant and Catherine Tate to look forward to, as well as Ncuti Gatwa's first episodes.
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Kingston reflects: "Even though I only actually worked on two episodes with David and Catherine, I really care about them a lot - and I'm always thrilled to see them, and I think it's fabulous they're coming back.
"David's going to be the Fourteenth Doctor! I can't wait! I can't wait to find out how that plays out, and then how Ncuti is introduced. It's very exciting."
As for any advice she has for the new actors, she recalls first meeting Smith and Gillan: "When Matt and Karen started on this incredible journey, we shot the first few episodes out of sequence. The very first episode that they shot on camera was the episode with River Song.
"The shoes that Matt had to fill, David Tennant's shoes - I'm not implying that David's got enormous feet - but they were very big shoes to fill, so it was decided that, I think it was episode 3 we shot first, that I would be there just to help and support them on camera for the first time in this world of Doctor Who - which I actually think was a very clever thing to do.
"To be perfectly honest, they didn't need it, they were perfectly fine, they didn't need me, but it was a lovely and very sensitive thing to have been considered.
"But I went out for supper with them, and I just sort of sat with them and just basically prepared them for the fact that their lives would never be the same again.
"Although all the rewards that will come to you from your performance will be amazing and will lead to incredible things, the beautiful privacy that you have right now in just being one face among many in a crowd, that will never happen again, so cherish it.
"That would be the same advice for Ncuti, although Ncuti's already well-known for his TV work. But nevertheless, this is going to be something different, totally different. The global reach that Doctor Who has is so huge and it's a wonderful, wonderful journey - but yes, his life will never be the same again."
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