I don't think this impact would be large at all for industries that approximate perfect competition like raw food. Price of such goods should approximate marginal cost. Marginal cost would only increase if workers in these industries could now demand higher wages than before, which doesn't seem likely to me unless the basic income is very high. Do you expect their wages to rise? If anything, I would hope basic income would go side-by-side with abolishing minimum wage, which could decrease the price of such goods.

You may very well be right for some other goods, but food is a good example where production can scale up but is essentially a no-margin industry. And it's a very important example in the context of eliminating poverty.

Of course, the only way to prove it is to try it out and see :)