You should report glass on pavements etc. to the district council, in this case South Oxfordshire. There is an online form at : https://forms.southoxon.gov.uk/ufs/ufsmain?esessionid=EAEA983857B7F51343BB9D61375AD669_1&formid=REPORTIT&SOVA_TAG=SOUTH
If this link does not work then go to the website and look at environment then street cleaning. Make sure you select street cleaning as this is the district council whereas the road maintenance is the county council.
In Didcot they are usually pretty good at responding to a request.
If it is a re-occuring problem then I would suggest you email Biffa at mailto:admin.southoxford@biffa.co.uk and copy in your local district councillor.
There is an identical arrangement for Vale of White Horse at: https://forms.southoxon.gov.uk/ufs/ufsmain?formid=REPORTIT&SOVA_TAG=VALE&SOVA_TAG=SOUTH and email mailto:admin.vale@biffa.co.uk