Both Cambridge City Council and South Cambridgeshire District Council (SCDC) (see councils for more on how these fit together) run a household waste collection scheme using green and black bins with the bins being emptied on alternate weeks. The green bin takes your compostable waste. The black bin is for general waste that can't be put into the green bin or green/black box.
In the City residents who do not have a place to store bins on their premises are issued with brown sacks for their compostable waste and white sacks for their general refuse. A maximum of five white sacks or six brown sacks will be collected at one time.
Exactly what constitutes compostable waste is quite subtle at the edges and rather than trying to track what the councils will accept on this page you should really visit the relevant page on the councils' own web sites which you can find here: City SCDC
(These pages have a nasty habit of changing URL so if you find the links above broken then please take a second to find the new location and update this page. Thank you.)