We are a family of four living in Derbyshire, we have 1 general wheely bin , 1 wheely for garden stuff and 1 wheely for plastic, tins and glass, I wrap up any foodie type stuff so that flies cant get in and we have no problems at all, if you dispose of carcasses and food direct and openly then you will suffer with flies and maggots, just wrap them up ,
If it is tight I get in the bin and compact it myself to make more room , that always works ( i believe you can buy a hand compactor for wheelie bins)
You could always ask the council for a larger bin of course so that could help you , failing that perhaps there is a neighbours bin you could slip some in ?? pensioners dont make much rubbish , not on there pensions anyway ....