The court directed senior registrar of the high court to communicate the copy of the order to jail and district authorities immediately for compliance.
Justice Mohammad F A Khan directed officials to bring Singh back to the jail by the evening after the cremation. Singh's appeal against his conviction in a criminal case is pending in the high court.
The rape survivor's family members sat on a dharna outside the hospital where she is undergoing treatment, demanding parole to her uncle. The Unnao rape survivor's family filed a complaint alleging "conspiracy" behind the Sunday's car crash.
Jailed BJP MLA Sengar and nine others were booked for murder on Monday, a day after the car in which the 19-year old rape survivor, her family and lawyer were travelling was hit by a speeding truck in Rae Bareli, killing two members and leaving her and the advocate critically injured.
The Uttar Pradesh government has recommended a CBI probe into the road accident.
The woman belonging to Makhi police station area in Unnao had alleged that Sengar, a four-time MLA who represents Bangermau in the UP Assembly, raped her teenage daughter at his residence in 2017.
The case had come to light after the victim allegedly attempted self-immolation outside Chief Minister Yogi Adityanath's residence.
Sengar, who is an accused in the rape case, was arrested on April 13 last year.