Its a fairly complex disease cycle, but the logic of badger control is quite simple
You've got infected cattle, and infected badgers, on the same land - you don't know which, originally, infected which, but its immaterial, you are where you are, both populations are infected, and both can successfully infect each other...
You get positive screening tests back, showing that some of your cattle are infected, you take the correct action, and cull the infected cattle - Hell, you could even cull the entire cattle population, and recolonise from another source that is known (and tested) to be clear.
problem is, you've still got a reservoir of disease on your farm, and unless you remove that - you're "sterile" population of cattle is going to become infected, as the remaining infected badgers will continue going round leaving urine trails packed with TB on the grass that the cattle eat.
unless you tackle both ends of the cycle of the disease, you'll never get rid of it.
The second issue, would be the biosecurity angle - if you've got clean cattle on one farm, and infected cattle on a nearbly farm, and never the twain shall meet, then the disease should not spread. However, if you've got your friendly neighbourhood badgers happily wandering between the two farms, then there's a problem...