The MOT is irrelevant. A car could have no working clutch or gearbox and still get through an MOT, for example.
There are plenty of things which could go wrong with a car but which, in the eyes of the people who design the MOT test, don't render it unsafe to drive. Such things aren't included in the MOT and, because 'advisory' notes have to relate to specific things within the MOT test, a tester who spotted a fault with a clutch, gearbox or engine (unless that fault affected the emissions) would not be permitted to mention it in the 'advisory' section.
On a legal point, you've clearly never reached the point where the law regards you as having 'accepted' the car (as being in the type of condition that you could reasonably expect a secondhand BMW to be in), so you're still within the period where you're entitled to a full refund of your money (rather than to a repair).
There are others on this site who are far more knowledgeable than me about how big a job it is to replace the fuel injectors but a quick look at some Youtube videos seem to suggest that it's a fairly straightforward task, which shouldn't require a great deal of labour. However googling for the cost of the parts suggests that they're far from cheap. This thread (from 2012) might give you a guideline as to the cost (and possibly also a warning about how warranty firms try to get out of paying all of it):
https://www.honestjohn.co.uk/askhj/answer/41796/my-bmw-s-injectors-needed-replacing---is-this-common-