Accounting degree vs apprenticeship Watch
You can't go into IBanking through an apprenticeship realistically (although whether you should be able to is another debate entirely) - there are maybe one or two such apprenticeships at a couple of high street banks in their investment divisions, that are no doubt highly competitive and I imagine leave you with little room to move elsewhere while you're on them or even after them. Goldman Sachs would probably still be happier to take the reasonable numbers of Oxbridge/LSE/top 3 Ivy League grads, and then those who got firsts from the other more desirably "target" universities after these, than someone who doesn't have a degree at all - all IBanking cares about is prestige, and you can go into IBanking grad schemes with a degree in underwater basket weaving, if it's from Harvard etc. If you were happy remaining at that institution or perhaps moving to a similar one then I guess it's fine, but the relative "prestige" and no doubt hence remuneration would probably be comparable to an accounting apprenticeship which gives you a lot more long term options, and there are more apprenticeships to choose from in that realm.
Quantitative finance normally requires a masters if not a PhD in a numerate subjects (such as maths, physics, engineering, CS, and a small number of Economics/Finance programmes may fit the bill - such as from LSE, Warwick or Cambridge), often with an emphasis on applicable mathematics/statistics and programming background (bearing in mind most of the indicated courses outside of CS and Economics will include some programming/computing elements at the undergrad level and will probably involve at least some computational modelling aspects in a PhD which would be relevant). I think you could go into some more quantitative areas of risk (and actuarial science roles generally) from undergrad with an appropriate background however. There is obviously no relevant apprenticeship for this - the nature of quantitative finance is such that you're actively "researching" and developing new quantitative models and programs/softwares and this kind of formal research and development is realistically on developed through at the least an undergraduate course, and as indicated realistically a masters and PhD. Of course once you go through all this, you have a great deal of options available to you - so even if you change your mind halfway along (and it's not a "short" path to be sure) you aren't left high and dry.
For Accounting on the other hand, an apprenticeship is a very valid - arguably better - option, compared with getting a degree. Normally it will take about as long if not shorter than the degree route, and you end up "skipping" several attrition phases if you're in a longitudinal apprenticeship program - i.e. at a major firm which will bring you up to the same ACA or what have you standard their grad schemes will do (a number of them I believe have the apprentices "join" the grad scheme cohort after a certain amount of time in the apprenticeship so you're basically the same at the point...). You can go into an accounting with pretty much any degree and it doesn't necessarily need to be from a top 5 uni (I know someone who went into one of the PwC grad schemes with a degree in History from an "average" RG uni).