Creating a reading group with one of my students I am currently a PhD student (on a teaching scholarship) at a UK university. A part-time MSc student in one of my classes has asked me for some advice on how they can prepare for their courses next year. I'd like to suggest that we spend some time over the summer (when there are no classes) learning something that would be mutually beneficial to us (in a sort of reading group style). I feel that this would be a good opportunity to motivate myself to learn some basic things that are missing from my education and also perhaps to make a friend. However, I wonder whether this would be unethical as it could potentially lead to this student having an "unfair" advantage over their peers? 

Note. Other PhD students in the department tutor some of their students privately (for money).
As far as having an "unfair" advantage by preparing over the summer is concerned, I don't think that having a "club" or some other form of advanced preparation is a problem. Studying in advance is not inherently unfair if anybody can do it. (Some students take a class that a grad school might require as an undergraduate; is that unfair as well?)

The ethical question here is whether or not you will be an active instructor for that student in the coming year. Showing favoritism to individual students that would put them in an advantage—or give the appearance of having done so—should be avoided. If you're not teaching them again and anyone who wishes to participate can join, then that mitigates the problem significantly.