Within the City, there is a fortnightly kerbside collection of plastic bottles (only). These go in the blue box. Beginning in October 2008 a similar scheme operates in South Cambridgeshire only there a second green box is being used.
Only plastic bottles made of PET (type 1), HDPE (type 2) or PVC (type 3), without lids, are accepted (more info).
At least some Tesco (Newmarket Road, Fulbourn) and Sainsbury's (Sidney St, Coldham's Lane) stores accept plastic carrier bags for recycling (maybe other places too). Some shops such as Arjuna on Mill Road accept carrier bags for re-use.