It's possible but the shock of white hair and the crazy eyes sound to me like a standard mad scientist character design. 

@col-klink True, but I'm pretty sure that stereotype was based on Einstein, and wouldn't have been solidly cemented as the standard mad scientist look at the time Lewis wrote Narnia. I can't think of many examples of similar characters who look like that in books or films prior to Lewis's time (which doesn't mean they're not there of course). 

If I remember correctly, in the book, Uncle Andrew mentions that he received a box from Mrs. Lefay, who instructed him to burn it. Then he discovered what was in it: it came from the lost island of Atlantis. Then he came up with the idea of the possibility of traveling to different worlds. 

If he was inspired by real magic, well, that certainly is debatable. Well, given that children and people in our world are exposed to Wicca and the occult in our day and age, obviously, people were during that time period as well. It is something to be aware of. I think Uncle Andrew learned the hard way that sometimes curiosity can get the best of a person if not careful.

As for science, well traveling between worlds isn't exact science. He could have been somewhat a mad scientist. At the start, he's been in his attic working on something.

It's one of those things that's hard to say, really. An interesting theory and certainly possible, but unless we can find evidence that C.S. Lewis definitely knew of Gerald Gardner and his ideas, it's only speculation.

I don't get the impression that occult practices and esoteric "magic" were nearly as prominent in the popular imagination during Lewis's time as they became from about the 1960s onwards, although obviously there were people who practised these things (including Gardner) well before then. I've certainly never heard of any critics, either at the time the Narnia books were published (the 1950s) or later, drawing connections between Narnia and the occult.

Lewis makes clear enough in the context of the story, in any case, that what Uncle Andrew is doing is foolish and dangerous — enough to warn young readers off trying such practices themselves, whether or not occult powers are real (a debatable subject and one I won't go into). And it wouldn't have been out of character of him to satirise an actual public figure, as Cleander says, but we can't (so far!) really say for sure.

I've always thought of Uncle Andrew as a more Dickensian kind of character, exaggerrated for comic relief. The part where he cajoles the children and later scolds them on their manners brings to mind the teachers and guardians (and often villains) of the various novels.

@courtenay Actually, to my knowledge occultism had a strong presence in elite society around Lewis's time. It hadn't quite taken over pop culture, but groups like the Freemasons, Rosicrucians, and the Order of the Golden Dawn were quite fashionable in high society from the Victorian period into Lewis's time. In fact, two members of the Inklings were involved in these groups. This has led some critics attempting to link Narnia and LOTR with the occult to claim Lewis and Tolkien were Illuminati or Masons 🙄 , but in reality these two Inklings were Charles Williams (a Rosicrucian) and W.B. Yeats (a member of the Order of the Golden Dawn, similar to the Masons.) In fact, W.B. Yeats would come into contact with the most notorious occultist of the century, the infamous Aleister Crowley, during his time with the order. He would actually go on to feud with Crowley, even engaging in "magical battles" with him... (not sure how all that worked). Crowley apparently had some dealings with Gerald Gardner, who eventually parted ways with him because (I suppose to Mr. Gardner's credit) he found Crowley's ideas a bit too dark and twisted. 

Reflecting on this, I wonder if this could also support the theory. If Yeats knew both Lewis and Crowley (and possibly Gardner as well) there's a chance Lewis might have heard about Gardner through him. Lewis as a Christian would have found many reasons to criticize the mindset of those attempting occult practices, but especially given the fact that some of his friends and associates had been mixed up in it, my guess is that he used the image of a "magician" currently growing in prominence to shape this cautionary character into a timely, relevant warning against what he saw as a dangerous rise in superstitious occult practices. 

@the-mad-poet-himself Very interesting and it certainly all sounds possible... it would be great to know if there's more than these bits of circumstantial evidence! I haven't seen this connection made in any Narnia commentaries or biographies of Lewis so far, though.

@courtenay Yeah, it's all just bits and pieces that can't lead to any definite conclusion - I just think they may make the idea slightly more plausible. I'd have to go over Lewis's writings that deal with his thoughts on the occult again to see if Gardner's name comes up - that would be to me the surest indicator. 

@the-mad-poet-himself Yes, that or perhaps any record (from someone who knew Lewis) that Gardner's name and ideas came up in discussions at meetings of the Inklings, for example.

I thought that Lewis was felt rather sorry for Uncle Andrew at the end of The Magician’s Nephew in saying that he became a nicer man. Lewis may have been thinking of magicians that are fakes in our world when he created him. He apparently used real Narnia magic in the story, but of course the story is fictional so Andrew was portrayed as a fool who was abusing magic. If you consider a fool who performs magic to be real magician then I guess that was what he was. I don’t think he was ever a respected wizard like Gandalf in Tolkien’s stories. He was more like someone who played with magic without knowing much about it. 🙂