The problem isn't the milk, and it isn't the meat. They are (generally speaking, in the UK), safe enough. It's the ownership of the rights over the cattle. Genetically modified lines are subject to patent law, and can't just be bred like ordinary cattle, but fees have to be paid to the owners of the IP. The long term strategy of the patentees is to own the rights to the national herd.

The more present problem, right now, is the treatment of animals with hormones and antibiotics, which damage humans heath both directly (your children ingest the hormones via the cattle products), and indirectly (the stupid use of antibiotics prove Darwin right by promoting resistant strains).

When the next trade dispute between the US and Europe erupts, remember that the milk and meat here are still relatively clean.