As for law, as long as you have a good GPA, you can do any undergraduate degree you want as there is no prerequisite. As for engineering, if you do one of the engineering system majors in Bachelor of Science/Biomedicine/Environment (eg. Chemical, Mechanical, Electrical, Bioengineering system, etc.), you can complete Master of Engineering in 2 years, but even if you didn't do one of the Engineering System majors, you can still do MEng but it will take an extra year.
Edit: all the graduate engineering degrees at UoM requires 2 units of first year mathematics (Calc 2 & Linear Algebra equivalent) and 2 units of first year science (Chemical & Biomedical & so on require Chemistry, some other streams require Physics, and for some streams any science will do.)