Why can't I have white plastic fillings at the back of my mouth?
You can, but not on the NHS. The NHS will not pay for white fillings at the back of the mouth unless you can demonstrate an allergy to mercury supported by a Consultant Neurologist's report to that effect. For the vast majority, then, this means, NO.
However, there is no reason why you can't pay privately to have white plastic fillings done. Discuss this with your dentist, he will be able to advise you of the prices involved and the suitability of any individual tooth for such a filling. White fillings start from about £25 and go upwards, depending on the size and position.