Well to address a few things:
- natural science is broad, and offers flexibility, it's very good if you don't know what you want to do. In what you might miss out by not doing 100% of one subject, you'll gain in having a broader scientific knowledge. There's lots of jobs in the chemical industry for instance that have next to no relevance to the undergraduate degree (i.e. polymer industry is huge, but most people will do very little on polymers, perhaps unless they end up in a polymer research group in their last year).
That said, a chemistry degree itself is broad, so add the range of combinations out of a natural sciences degree to that and i'm unsure what routes it keeps open and which it doesn't. The course has a decent reputation though so I wouldn't necessarily worry. Given the institutions that offer the degree I think you'll be in a fine position. I would have a look how much lab work you get in the course, and directly compare how much of what area is covered (i.e. physical chemistry, organic chemistry, inorganic chemistry). Lab work is what you're paying for in the degree, in my opinion. You can't do that on your own, but you can study from a textbook all you like. It's also the most engaging part of the degree.
What do you mean by continuing into other areas? What sort of areas?
ChemEng - it's more engineering, with some chemistry thrown in. Basically more involved in the scaling up and manufacture process. At my current job I actually think the chemical engineers spend more time at their desks organising things, optimising processes and looking at theoretical approaches, rather than doing lab work. It depends on the job, I don't know too much about it myself, so have a google around and get a feel for it. There's a few threads around here on the engineering forums that will probably give you some insight from current/previous students.
Maths and CompSci - I guess it's just if you like programming and want to go into IT/development. I know a couple of people who did it and they enjoyed it, but it wasn't a difficult decision for them. I would say though, personally, it strikes me as an industry (programming-wise) that you can access by learning the skills yourself and demonstrating it. A degree is the easiest way to do it all but I guess if you're not convinced it's for you then eh...