Can Barristers pick and choose their cases?

Im thinking of becoming a Barrister in Criminal Law, im just wondering if Barristers have the option of NOT choosing to represent someone in a case? For instance, i wouldnt want to defend say, a paedophile. Is the option there to refuse the case or does the Law firm im in demand that i take the case regardless. I know many Barristers are self-employed but im more intrested in joining a Law Firm. Any advice and help would be really welcome and grateful. Thanks