Can i sue for my name been slandered?

was working at sky tv and was only there 3 weeks when i was taken from my training and told that some one had put in a complaint about me. T hey had over heard me in a private conversation on my break(unpaid) when i mentioned this place is full off nancy boys i admited that i did say this but was never given the oportunity to explain what i was talking about, i was talking about my younger brother who had went out on night out with his mates in newcastle and they went into a gay bar and it was full of gay men and my brother ran out of the bar saying this place is full off nancy boys, i was never given the chance to explain this now a year on i applyed for to work there again and was told i could not because of uall discrimination and i would never work there again can some one please help me as i have done nothing wrong and i am not a ually discrmitive person i am quite the opposite as it dosent bother me , many thanks