The former Cambridge University student, from Stratford-upon Avon, in Warwickshire, had been working as a volunteer as part of the Learning Together prisoner rehabilitation programme, police said.
Jack Merritt, 25, another former student who was involved with the programme as a course coordinator, was also killed in the attack on Friday afternoon.
The graduates were at an event to mark the fifth anniversary of the programme at the Fishmongers’ Hall in the capital when the attack began to unfold shortly before 2pm.
Ms Jones’ family described her as a “funny, kind, positive influence at the centre of many people’s lives”.
“She had a wonderful sense of mischievous fun and was generous to the point of always wanting to see the best in all people,” they added in a statement.
“She was intent on living life to the full and had a wonderful thirst for knowledge, enabling her to be the best she could be.
“Saskia had a great passion for providing invaluable support to victims of criminal injustice, which led her to the point of recently applying for the police graduate recruitment programme, wishing to specialise in victim support.
“This is an extremely painful time for the family. Saskia will leave a huge void in our lives and we would request that our privacy is fully respected.”
David Merritt, the father of Jack Merritt, from Cottenham, Cambridgeshire, announced his son’s death on Twitter on Saturday, paying tribute to his “beautiful spirit”.
In a statement released on their behalf on Sunday, Mr Merritt’s family described the 25-year-old as a “beautiful, talented boy”, who died “doing what he loved”.
“He lit up our lives and the lives of his many friends and colleagues, and we will miss him terribly,” the statement added.
But they asked for his death not to be used to justify introducing “even more draconian sentences” on offenders.
The statement continued: “We know Jack would not want this terrible, isolated incident to be used as a pretext by the government for introducing even more draconian sentences on prisoners, or for detaining people in prison for longer than necessary.”
Dr Vin Diwakar, the medical director for the NHS in London, said on Sunday that one of the three people injured in the attack had been allowed to return home while the other two remained in a stable condition in hospital.
Stephen Toope, vice-chancellor of Cambridge University, confirmed one of the three people injured was a member of university staff, adding that the university “condemns this abhorrent and senseless act of terror”.
Convicted terrorist Usman Khan, 28, was at the same event as Ms Jones and Mr Merritt when he reportedly “threatened to blow up” the building near London Bridge shortly before 2pm on Friday.
Armed with two knives and wearing a fake suicide vest, he killed the two victims and also injured three other people before being tackled to the ground by members of the public and then shot dead by police on London Bridge.
It later emerged that Khan, who was on licence and wearing an electronic monitoring tag, was a convicted terrorist who was released less than seven years into a 16-year prison sentence for plotting to bomb the London Stock Exchange.
Friday’s knife attack has triggered an urgent review of terrorists released from prison.
London Bridge was one of the scenes of a terror attack in June 2017 – also during a general election campaign – when eight victims were killed along with the three terrorists, who were armed with knives and wearing fake suicide vests.