I used to work as a buyer/business developer for a veg box scheme (that shall remain nameless) in London. I'm off to Moscow for work for a week, but I'm happy to answer questions to the best of my ability when I return.
For now, suffice to say that it can be a very tricky business. Depending on your market of course, but people wanted certain staples all year round which were often difficult to source, freshness along the supply chain was a huge problem, and customers often wanted supermarket standards of cleanliness, for local market prices.
I did a bit of business with Riverford, and I know that they invested hugely in their packing and cleaning operation to address some of these issues.
Payment is also a problem. The best scheme I ever saw never handled a pound coin - everything was done via direct debit. However this meant that they didn't reach anyone who had low or irregular incomes. Processing cash, cheques and DDs cost our scheme a huge amount - we had a very large back office.
Another scheme that I admire hugely, based in Dublin, old friends of mine, have a social agenda. They distribute a lot of boxes via a women's refuge - figuring that people in that situation need good food.
In short, you'll need to do most of your work before you put a seed in a pot. Who is my market? What do they want? What spread of veg and seasons can I cover? How do I control quality? How is my credit control? This applies even if it's a really small, local scheme.
I'll be back in a week if you want to carry on the discussion.
Best
Oscar