Yes you could do a basic game engine in your final year and maybe even a game that effectively uses your engine. Yes this would be an achievement but would it be academically suitable for a final year project?
I'm afraid not.
A basic 3D games engine can nowadays be developed from scratch using books and online resources pretty much like reading a recipe book. Lots of hobbyists do it in their spare time and nearly everybody applying for a graduate position has some form of "Engine" that they have written in their portfolio.
I'd expect you to be able to create a basic 3d engine as part of one of your course module but, for a final year project I'd expect something a little more advanced and more research oriented and a lot more focused. Maybe creating a new advanced feature for an existing engine. Or maybe just writing the renderer component of an engine and really focus on just this component. Your final year project should be more focused in one area, perhaps graphics, physics, sound, AI, world representation or gameplay scripting. Writing a full engine is like having to write lots of components but you won't be able to drill down deep enough into any one component to make it academically rewarding.
I want to get into the game industry. For that i need some work in this area. I chose "engine" as a project becasue i would be able to use it in my portfolio when applying for a game development company and it will work as my final year project. As far as going for something bigger, I have cleaned a lot of things from our "engine". It is basically now a renderer. With a somewhat more focused target, I think we'd be able to create something with better quality.