Your teacher is wrong. Depending on the level 3 apprenticeship scheme, the employer and the level of apprenticeship, continuation of your education at Bachelor's level and above is possible (whether that is company sponsored or otherwise).
Apprenticeship schemes at level 4 and above will have a foundation degree and/or Bachelor's degree component to them, meaning you will actually study for an Fd or Bachelor's degree as a part of the apprenticeship scheme itself.
The quality of apprenticeship scheme varies between employers and training providers, so it is really important to do your research before making any decisions (as you would for a university course, or any other major decision for that matter).