Despite what was depicted in this episode, Lady Margaret Beaufort died two months after her son.
Edmund Dudley was absolutely not arrested, tried and executed in a single day. Though he was in fact charged with constructive treason, he was imprisoned in the Tower of London for over a year before his execution in August of 1510.
When Margaret Pole realizes she is in her late brother's cell after seeing his name carved into the door. However, the Earldom he used as his last name for some reason is misspelled as "Warrick" rather than "Warwick." The closed-captioning repeats this mistake throughout the series.
Margaret Pole was not arrested for treason or held in the Tower at this time in history. She remained in an abbey until Catherine of Aragon paid her debts and restored her to favor. She was not even suspected of treason until around 1538 when her sons were accused of allegedly conspiring to overthrow Henry VIII.