I always thought this was my secret idea from back in early '60-ies
Mylar was not know to me then.. but, as Ken suggested, my conclusion after some experimentation with various materials and methods was that it would be impossible to obtain the quality, not to mention the coping with variability of the optical surface shape due to temperature and air pressure changes (I imagine even air circulation may be detrimental to the resolution of such a mirror).
While playing with this, one friend of mine suggested electrical field as a mean to obtain curvature (high voltage, in other words - couple of kV.
BTW, electrostatic loudspeakers use the same principles for sound generation).
However, I also remember one S&T article on ATM - there was a description of pre-distortion of flat glass plate by means of attached low pressure chamber, used in process of figuring of Schmidt correction plate.