The Police And Criminal Evidence Act of 1984. It sets out the rules by which people have to be treated when they're arrested, interviewed, detained, searched - if you get it wrong, whole cases can collapse. In this case, the police officer didn't caution the suspect before he gave his confession and it could be argued that he withheld legal representation from him as well. Even though he confessed, that evidence can't now be used because the suspect refused to sign the notes or confirm that what he said was true. Basically, if they don't find enough forensic evidence to convict him, he could get away with it.
I don't know what happened in the real case, btw, so that's not a spoiler, just me speculating!