The dangers of increasing antibiotic resistance are well known. It is impossible to use the NHS without becoming aware of the comprehensive warnings relating to the improper prescription and use of antibiotics. The danger is that improper use of antibiotics will result in antibiotic-resistant strains of harmful bacteria arising - and antibiotics, which have proved the mainstay of public health for fifty years, will no longer be effective.
People are less aware of agricultural use of antibiotics, to promote growth in healthy animals. Here is an article on the subject from Wikipedia, and here's an introductory article from The Guardian. Theoretically, the practice should be being reduced. This article from The Independent suggests that disturbingly, even antibiotics of last resort are still being used to promote growth.
There is no way of telling from meat labelling what role antibiotics have played in the rearing of animals. Some food suppliers are now drawing attention to their decision not to use antibiotics in farming (eg. Karro Food Group, who even sought to establish a trademark for antibiotic-free meat). A preferable way forward would be for meat from animals reared using antibiotics to promote growth to be labelled as such. I have started a petition (here is the link) suggesting this form of labelling.
This would promote consumer choice and information. Another issue is that when we leave the EU, the government has indicated that it wishes to have a comprehensive and liberal trade agreement with the USA. Use of antibiotics in meat-farming seems to be considerably more widespread there. A consumer regime which makes this visible would hopefully help in the fight against the growth of antibiotic resistance.