The group will make a claim against Probus, the insurance company for Hertz, to pay for medical costs.
Terrorist ringleader Khuram Butt, 27, hired the white Renault Master van hours before launching the attack which killed eight people and injured dozens more.
He, Youssef Zaghba, 22, and Rachid Redouane, 30, ploughed the van into pedestrians on London Bridge - killing Xavier Thomas and Christine Archibald and injuring several other people - before stabbing passers-by at random near Borough Market.
"This atrocity has had a profound impact - both physically and psychologically. It will take a great deal of time for survivors and relatives of those who died to begin rebuilding their lives.
The law was changed in 2017, just before the Westminster Bridge attack by extremist Khalid Masood, to allow victims of terror attacks to make claims against car rental companies.
However Mr Maguire warned that this has created a two-tier system, because those who were stabbed have to claim from the Criminal Injuries Compensation Agency, which provides smaller payouts.
Mr Maguire, who also represents victims stabbed by the three jihadis, said: "These tragic events expose a stark two-tier system for compensating victims of terror attacks.
"Those hit by van are able to pursue a normal civil claim against the insurer, which means we are able to quickly secure vital financial support for ongoing care, rehabilitation and loss of earnings.
"However, those stabbed can only pursue the Criminal Injuries Compensation Agency, meaning financial support is far more limited, with no assistance with their rehabilitation or financial losses.
"It's difficult to explain this to a client who was stabbed that they're likely to receive much less help and financial support than someone hit by the van - they rightly don't see how that's fair."
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