I would suggest that you try your best to talk your maths teacher into predicting you an A and apply this year anyway (even if they don't it could be worth the try just for the UKCAT/BMAT practice and maybe interview practice as well if you get through).
If you don't get the predicted grades that you want then you could always work really hard this year to get a minimum of AAA with your A Levels and then just take a gap year and apply next September (which could increase your chances as you'd have more opportunities for work experience and things).
Would your teacher be more likely to predict you a higher grade if you agreed to retake some of your AS Level modules?