However, the Met said it had decided to “instigate judicial review proceedings” over the officer’s reinstatement.
The independent panel concluded in June that “a flawed structure” had led the force to sack 56-year-old Ms Williams after her conviction for possessing an indecent image of a child. It determined that her dismissal should be replaced with a final written warning, clearing her to return to work.
Ms Williams’ trial heard she received the video via WhatsApp from her sister who had been sent the clip by her boyfriend.
The officer said she had not viewed the 54-second video and did not know it was on her phone.
But prosecutors said there was no way she could have missed it, and cited a response from the officer to her older sister to “please call” as evidence she wanted to discuss the content.
The jury was told experts had not been able to examine Ms Williams’ phone properly.
She was sacked by the Met after a special disciplinary hearing concluded her behaviour amounted to gross misconduct.
The Met found that Ms Williams’ actions were likely to undermine public confidence and had not been a “trivial lapse”.
In a statement, the Met questioned the judgment of the Police Appeal Tribunals (PAT).
It said: “The PAT has made findings in two separate cases that overturned carefully considered decisions to dismiss officers from the Metropolitan Police, which had been made in special case hearings following criminal convictions.
“The special case hearings had deemed that the convictions amount to gross misconduct, and that the officers should be dismissed. In both cases the PAT did not agree with these findings and replaced the officers’ dismissals with a final written warning.”
The identity of the other police officer has not been revealed.