As has been said The Soil Association provides lots of information. Some other links include:
A short fact sheet for schools: www.face-online.org.uk/resources/factsheets/discovering/organics.pdf
Summary info from the Food Standards Agency (note that their remit is food safety, they have nothing to say about environmental impact). If you scroll down there is a link to more info on milk: www.food.gov.uk/foodindustry/farmingfood/organicfood/
Links to lots of other organistions from Defra, who regulate organic and other farming in the UK. If you look around their site from here you can find some detail via lots of dry policy papers, if that interests you! archive.defra.gov.uk/foodfarm/growing/organic/links.htm
I'm disappointed not to be able to find a good public summary of the environmental benefits on the Natural England site (statutory conservation body) but the RSPB offers a summary and will have more in depth info if you want to search: www.rspb.org.uk/ourwork/farming/policy/systems/organic.aspx
The Soil Association and other UK organic certification standards are very high and, as others have said too, exceed free range welfare standards. There are lots of other certification schemes in other countries, which have varied standards. Buying British-produced organic is a good idea for this reason, as well is reducing transport (though for conventional foods, food-miles can be a bit of a red herring, with more fossil fuels used for fertiliser and heating in European greenhouses than for production and transport from Africa. Anyway...).
Local produce, especially if you have the luxury of some knowledge of the producer, is a great choice. We chose a veg box scheme from a farm about 10 miles away that is almost all their own produce, the rest from within the county. We get really good variety and value.
Maybe you can report back on what you find out and decide?