I've done an accounting related undergrad, and then I did economics and finance related postgrads, althought not at King's
The course can be great if you intend to go into accountancy, but there are cheaper and faster ways to get qualified. The sort of master's you can do is limited to either accounting, finance, and management to my knowledge (there might be other postgrads that won't require any subject specific degrees at undergrad, but I haven't checked). I don't see the point in doing a master's in accounting though, because you're mor or less covering the same material in the undergrad and you won't get any more exemptions for your professional accounting qualification. I'm also not keen to say you should do finance as a master's because similarly it will cover similar content as the undergrad, and you won't need it to go into the finance sector, where they have a myriad of Level 3 qualifications to get into a lot of finance related jobs (most of which have little to no entry requirements). The only qualification that I know of that would require a degree of some sort is the CFA, but even then you can get around that by doing the IMC that doesn't require an entry requirements.
Whether you will enjoy accounting and finance will depend on your personality. Personally, if it doesn't have quantitative calculations, and is more perscriptive and more rules based like a law subject, I would hate it. So I ended up liking the management accounting, stats, economics, and finance modules a lot more than the financial accounting. I didn't do any law modules, because you would understand I would avoid them like crazy. Having done accounting modules outside of uni, I can say I'd avoid audit like the plague as well.
In order to do some master's in economics, you will need to do a conversion course (PGDip) after your bachelor's in accounting and finance, because you won't have enough accounting knowledge in your undergrad to do a master's in economics. If your undergrad was in economics and accounting or economics and finance, then you should be able to do the master's in economics or economics and finance. Most top universities don't usually offer this option at undergrad though.
My question to you is why are you choosing to do these set of degreees? If you intend to go into research, then the economics undergrad is more than sufficient. If you intend to go into accounting, you might want to decide on the professional body, and choose modules that are more aligned with the body (although it will be cheaper and possibly quicker if you go straight for the qualification instead). You can also go into accounting research after you have done your accounting qualification.