Thanks, Warbs. I've just toddled off and Googled it, and it's the Fairtrade (all one word) Foundation, and it explains its remit and ethics in an excellent website. It does, interestingly, expound in some detail about why it doesn't apply its Fairtrade logo to UK milk farmers - the reasons mostly being that our farmers are supported by a number of social benefits which foreign farmers aren't. However, it does say that it supports any effort to try to bend the government towards fairer trading practices in British milk production.
I think there is the strong possibility that 'fair trade' and 'Fairtrade' would be confused quite easily and it might be better if the British producers came up with a new slogan/logo, like "Better Deal" or something like that. However, I've signed the petition because I don't like to see how hard people work, invest their entire lives and money into their dairy herds, comply with DEFRA's 5,829 edicts and try to keep up with its constant changes to those rules and regs, and then get offered the lowest-possible denominator by massively powerful superstore chains. Fair deals, yes - for all.