The BBC Trust tonight said it has ordered an on-air apology to licence fee payers for "serious and deliberate breaches" the BBC editorial guidelines.
Setting out a plan of action, it also asked director general Mark Thompson to write a personal apology over the scandal.
The Trust said it endorsed a statement made by chairman Sir Michael Lyons on its behalf into the "deplorable intrusion" caused.
The statement read: "The BBC Trust represents licence fee payers and on their behalf has a responsibility to safeguard high standards of BBC broadcasts.
"The Trust is dismayed both that the offensive comments broadcast on the Russell Brand Show on 18th October fell so far short of audiences' legitimate expectations, and by the deplorable intrusion into the privacy of Mr Sachs and his granddaughter.
"The transmission of these comments via a BBC Radio programme represents an abuse of the privilege given to the BBC to broadcast to its audiences.
"On behalf of the BBC, the Trust offers a full and unreserved apology to Andrew Sachs, Georgina Baillie and the rest of his family.
"The Trust extends this apology to licence fee payers as a whole."
The Trust's editorial standards committee will review the issues further at its meeting next week and it has requested a final, written report from the director general at its next meeting on November 20.
The Trust described editorial control and compliance procedures in non-news areas of the BBC's Audio and Music department as "inadequate and need to be strengthened".
It set out an initial set of actions it needs from from the director-general.
The Trust said: "We have asked the director general to present formal recommendations to strengthen editorial controls and compliance for the Trust's consideration at our December meeting.
"Once approved, the Trust will independently validate the effectiveness of these measures after they are implemented.
"Furthermore, we have requested the executive to strengthen immediately the editorial controls around any programme which represents high levels of editorial risk.
"Also in this area, we have asked the executive to assess immediately the editorial controls and compliance procedures in place for all programmes - across television and radio - where the production company is owned and/or managed by the featured performer."
It said the incident "has underlined the importance of editorial boundaries for high-risk broadcast material".
"We will therefore make this a central plank of our scheduled review in 2009 of the BBC's editorial guidelines.
"Key to this must be a common understanding within the BBC of what is acceptable and this must reflect widespread public opinion."
The Trust asked the executive to issue an on-air apology to licence fee payers on BBC Radio 2 "for the serious and deliberate breaches of the BBC editorial guidelines on offence and privacy".
The form and timing will be agreed by the Trust's committee.
The Trust continued: "We have also required the director general to write personally to Andrew Sachs and Georgina Baillie to apologise on behalf of the corporation.
"The Trust's job is to ensure that the BBC provides a wide range of programming to reflect a diverse society made up differing ages, interests and backgrounds.
"In doing so however, it is essential that the BBC demonstrates its commitment to the highest level of editorial standards at all times.
"The BBC has fallen way short of the public's overall expectations in this case, and it is essential that lessons are learned to avoid further lapses in the future."