She made aliyah at the age of 86 in 2009.
AJR chief executive Michael Newman paid tribute to an “inspirational” figure.
“As one of the older Kinder on her transport, Bertha looked after the younger children on the journey. Poignantly, her passing came on the anniversary of the arrival of the first Kindertransport in 1938.
“Although she endured great personal tragedy throughout her life, Bertha was an elder sister to many of the Kinder and a popular presence at the AJR day centre and our gatherings.
“Such was her charm and powers of persuasion, it was impossible to refuse her requests.”
Tribute was also paid by Holocaust Educational Trust chief executive Karen Pollock, who said Ms Leverton had “worked tirelessly to reunite and support other Kinder refugees.
“Our thoughts and prayers are with her family, friends, and all those who knew and loved her.”