@tomcritchlow, I just built an online markdown converter to HTML, (see MarkMe! - A lightweight and simple markdown to HTML viewer and editor online for more info). I used a package called markdown-it and it’s completely front-end. You can refer to the source code if you’re not comfortable with Node.js, as I’m using the package with client-side JavaScript.
All the best for your project, I’m looking forward to its completed version!
P.S.: The tutorial above does have a lot of unnecessary stuff. The markdown viewer I built is similar to the tutorial but with less code and more features.