By Core, do you mean pure? The only way to really check is to look at departmental websites.
In general, you can expect a big department to offer a first year consisting of roughly 60% pure (counting calculus as pure), 15% Stats & Mechanics each, and 10% miscellaneous stuff like software tutorials. Then in your second year there's the first opportunity for specialism, and by the third year there is usually an equal choice of stats/probability, Applied, and Pure options.
On the other hand, smaller departments have a tendency to lean one way or another in terms of how much you can specialize and what options you can choose in the third and fourth years: for instance, Lancaster leans in the direction of pure and statistics, UEA towards Pure and Applied, and Kent towards Statistics and Financial mathematics with a bit of pure foundations.