Whoever said about Big 4 route into an IB is correct unless you are looking for a career in middle office which is fine but I'm guessing that this post being on a trading forum, the waterlily doesn't want to do that!
At the IB i used to work at, CIMA or ACA grads both inhabited the (proper) IB side of the business. In short, if you want to go into corporate finance etc then accounting is the path.
If you want to go into something more market-based ie trading, asset management then CFA (after IMC or SI exams) is definitely the better choice as it will be seen more favourably plus it'll be a broader learning experience.
Also, a masters (at a good school) may get you where you want to go a lot quicker than additional accounting courses at LSBF.......assuming you're not doing a masters at LSBF!
Just my tuppence!