Positron lifetime measurements on poly(isobutylene) (PIB) and cis-trans 1,4 poly(butadiene) (PBD) have been performed in a wide temperature range. The effects of light illumination on the positronium formation at low temperatures were investigated. At 82K in darkness, an increase with measuring time of the o-Ps intensity was observed in PIB, but not in PBD. The enhancement in PIB could be quenched by exposing the sample to visible light. The results are interpreted in terms of the accumulation of shallowly bound electrons, created by the positron irradiation itself and the bleaching of these electrons by light. The influence of the positron irradiation on the molecular weight distributions of the specimens was investigated by size exclusion chromatography. During a series of positron lifetime measurements the PIB sample degraded due to the positron irradiation, the degradation being much faster at high (T > 300K) than at low temperatures.