If the defendant has entered a guilty plea there won't be a trial.
He'll no longer be an unconvicted remand prisoner but a convicted prisoner, held 'on judge's remand', awaiting a sentencing hearing.
Since the CPS no longer have to complete the preparation of their trial documents, and his defence team no longer need to prepare a defence, all that is left now is for the preparation of pre-sentencing reports from the probation service (and from any other source which the judge has called upon, such as a psychiatrist) and for his defence team to ensure that they are ready to present any mitigating factors (and/or character references). That's likely to take around 4 to 6 weeks.
Chris