On the maths side it's usually pretty similar across unis, you'll probably revise your calculus knowledge of differentiation and integration, and usually extend your knowledge of single variable integration techniques to further maths topics (volumes of revolution, integration of parametric equations, using partial fractions in integration, integrating less straightforward functions requiring more manipulation to get them into an integrable form), maybe also t-substitutions. You'll also cover matrices and complex numbers, then begin a long love affair with differential equations, which is a pretty extensive topic and will go well beyond the simple variables-separable equations you might do in FM.
You'll later do multivariable calculus and vector calculus (although the latter might not really be covered until second year). You'll also at some point go over different coordinate systems (polar/spherical/cylindrical) with applications in calculus problem usually. Pretty much everything from this website:
https://tutorial.math.lamar.edu/ will be covered in the first year or two. The Schaum's Outline of Advanced Mathematics for Scientists and Engineers also covers more or less everything you might potentially cover in the mathematical methods of most enginering courses in the first two years (some won't cover all the topics and maybe places like Oxbridge/Imperial will have slightly more than that; it's worth getting a copy as it's a good revision resource though!).
On the engineering/science side it can vary a lot more. You'll probably review A-level mechanics (both the kinds of things you've done in physics and in maths) and move towards a more mathematical (calculus based) treatment of these (especially for dynamics). You'll probably also be introduced to fluid mechanics and the mechanics of materials, and maybe some more materials science-y topics too (in terms of the properties of materials, crystal structure etc). You might also do thermodynamics, probably in conjunction with fluid mechanics (if you don't do it in first year you'll almost certainly do it in second year). Most if not all of these topics will use the aforementioned mathematical methods pretty fluently (e.g. calculus and vectors for mechanics, differential equations for fluid mechanics, maybe some matrices type stuff with the materials side of things).
Also you'll usually have "engineering design" type work and labs. These can vary a lot and I don't really remember the mechanics labs from when I was doing engineering, on the engineering design side you'll probably start learning to use various CAD softwares (e.g. AutoCAD, SolidWorks, similar) and then designing in those using the engineering science principles and mathematical methods you've studied. The labs will probably require you solve some scientific/mathematical problems in order to set up the experiment and then you will complete the experiment and write it up with all the mathematical working and scientific principles explained in a lab report afterwards.
You might also have some slightly more bull-*****y "professional practice" or "management" modules where most people kind of just zoned out because they were really easy and it was just learning what Gantt charts are, some basic principles of project management, and how to use Excel for more than just simple formulae. Sometimes these also include some slightly more useful content such as learning some basic principles of programming or how to use MATLAB or similar softwares too, if this material isn't fit into other modules or taught later in the course.