From dj's link "The coffee brand Café Mam [Mrs Corbyn's brand] which was featured in the article is not a Fairtrade licensee and is affiliated with a different certification body. However Indigenas de la Sierra Madre de Motozintla (ISMAM), the producer co-operative in question, does sell very small volumes of coffee on Fairtrade terms. Unfortunately it seems the resulting return for their hard work is not enough to cushion them against the knocks they currently face.
In the past, ISMAM’s Fairtrade sales have provided higher incomes for farmers, technical assistance and training in organic production and sustainable farming.
Furthermore, the article doesn’t provide a like for like comparison of the final coffee price. The article compares roasted coffee vs the coffee delivered by the producer, which only has part of the process, leaving further processes without consideration (dry milling, roasting, packing, transportation, etc.).
If you buy wheat, say, grind it into flour and bake it into bread, there are a lot of processes in between harvest and final product to be paid for as well the sacks of grain. Same is true of coffee from bean to jar.