Hello!
Your undergraduate performance is one part of your overall application. As well as your grades, your proposal, references, movitation and other academic / professional activities (you've got three years -- who knows what you might get up to in that time?) will all be important.
If you achieve a First, especially if combined e.g., with some excellent individual module scores, this is not going to be a significant limiting factor. In fact, to try to improve access to postgraduate HE, both Oxford and Cambridge are, in different ways, trying to be more flexible about how they evalaute candidate's undergraduate institution.
That said, these courses are, as you know, competitive! I think the key will be making the most of where you are to learn what you can and demonstrate a significant motivation and interest in your subject. SOAS is a wonderful place to do that. Being in London, you will also be surrounded by all kinds of seminar series, research projects, and other academia-adjacent activities (internships, conferences, events) that you can get a taste of, and may help to give you a 'hook' in terms of what you might want to pursue in a masters.
Enjoy!