Chemistry + Maths at Uni Watch
It really depends on the flavour of the degree; more physical/theoretical chemistry oriented courses (or which have those options and research groups in the department so someone is teaching the courses) will by virtue of this require more maths. More synthetic oriented ones don't really require or use it as much.
Often you might get introduced to some basic group theory in higher level inorganic modules, and in physical you'll at least need a basic introduction to vector calculus (and by extension multivariable calculus and a good background in vectors and maybe a touch of linear algebra proper), differential equations, and complex numbers to cope with the quantum chemistry stuff and the Schroedinger eq. Some might like to do the matrix version of things and will include that as well.
None of this is really considered "maths" in the sense of university level maths; these mathematical methods are useful in this context but uni level maths typically concerns itself with the underlying mechanics of the calculus at play here (and fundamental algebra for that matter) which a joint honours type course would include more of. The usefulness of this as a career chemist is somewhat limited in industry and debatable in academia (depending very much on your area of research, and even then only the more theoretical physical stuff uses that extensively, and most of those people were physicists rather than chemists).
You'll probably find you'll have to do some maths modules as methods type courses and this is more in line with the type of stuff you've done at A-level (and probably enjoyed), and you may have the option to take some more courses in this vein if you so choose as optional modules. For example, again with southampton, I'm fairly certain you have to do one maths methods course in first year, and you can do a second if you want. If you do both first year ones, you can do one in second year, and potentially pick up a couple of the more methodsy/applied maths courses from that as options beyond that.
If you really like the applied maths stuff (or even the more theoretical, abstract stuff) then physics might be worth looking into too
While of course there are common threads ChemE will be a lot of applied fluid mechanics and thermodynamics/kinetics, chemistry will some of the latter, along with inorganic and organic chem and quantum chemistry.
Chemical physics will focus on the thermo and quantum aspects of chemistry as they relate to chemistry in general (typically inorganic and materials chem more than organic chemistry).
Of course in that vein there's also materials science which on a tokenistic level includes stuff from a chemistry and maths background.
They also all train for different roles (while all could be used as a springboard to academia, chemical physics/chemistry with physics is probably stronger there if you plan on going into physical chemistry academia compared to any other).
Chemistry with maths is probably the odd one of the bunch as in this context it's essentially two separate subjects combined, and the overlap is up to you to find moreso than the others. If you have long term DISCRETE interests in the two, that's certainly a viable choice. If you just like doing things in a quantitative way using mathematical tools then picking up maths methods courses in a general chemistry degree, or looking at chemical physics/chemistry with physics would probably be more appropriate.
Have you considered any physics/chemical physics courses? They would undoubtedly be more maths-heavy than almost all straight chemistry degrees.