An identity parade is usually only part of a police investigation. The suspect will usually already be under arrest and if as a result of a parade there is sufficient evidence to support a charge (as assessed by the CPS) it will be laid.
As far as remanding in custody is concerned the police take the initial decision whether the suspect is kept in custody or released on bail. To keep the suspect in custody they have to have grounds to believe that the suspect will either abscond, commit further offences or interfere with the course of justice. If refused bail by the police the suspect must appear before the first available Magistrates’’ court and in any case in no more than 48 hours. If the case is not concluded at that first hearing the Magistrates will decide on bail or a remand in custody and they will use the same criteria as the police.