Does my degree in (Finance/engineering/physics) prepare me for the MSc Statistics course?
We usually ask for a 2:1 honours degree, or equivalent, with substantial mathematical and statistical components or a pass at an equivalent level in the Graduate Certificate.
The School of Mathematics and Statistics provides some guidance for what you should already know for a Statistics MSc course. You can find that here: https://www.sheffield.ac.uk/maths/masters/papers.
If you don't feel like you're ready for the MSc course after looking at that material, the department also offers a Graduate Certificate in Statistics. Which would provide you with everything that you need for starting an MSc in Statistics. There is information about that here: https://www.sheffield.ac.uk/postgraduate/taught/courses/2021/statistics-pg-certificate.