Campaigners successfully challenged the government after it overturned a decision by Westminster Council to refuse permission for the monument.
The London Historic Parks and Gardens Trust described the process to approve permission as “flawed”.
The charity, which launched the case, argued the project was the “right idea, wrong place”.
It opposed the UK Holocaust Memorial and Learning Centre being built in Victoria Tower Gardens, a small triangular Grade II-listed green space next to Westminster Abbey and the Palace of Westminster.
The trust’s lawyer, Richard Drabble QC, argued it did not comply with a 1900 legal act affecting park land, which contains “a prohibition on using Victoria Tower Gardens as anything other than a garden open to the public”.
The monument was set to include 23 bronze fins and an underground learning centre.
Former Prime Minister David Cameron announced plans for the memorial in 2016 but disagreements over its meaning, public safety and potential harm to parkland have followed the project.