The bill is said to include £15,500 spent by the Royal Liverpool Hospital transferring and securely storing the child killer’s corpse after his death at the high-security Ashworth Hospital in May.
The figures were obtained under Freedom of Information laws.
The Scottish-born child killer, who used the name Ian Stewart-Brady, is reported to have left several thousand pounds in his will to animal charities.
Terry Kilbride, whose 12-year-old brother John was one of five victims of Brady and Myra Hindley, said: “No one should have to pay any more for him.”
Brady was buried at sea under a shroud of secrecy after a judge ordered he should be cremated with no ceremony, no flowers and without fulfilling his wishes for a particular piece of classical music to be played.
Court documents released in November showed the secret operation was carried out under police guard on late on October 25.
The cremation at Southport Crematorium is reported to have cost £1,070.
The killer’s ashes were then taken out to sea from Liverpool Marina by boat and jettisoned in a biodegradable urn made of rock salt – said to have cost £35.
The bill for Merseyside Police’s services after Brady’s death was £2,570.40.
The Royal London National Funeral Cost Index, published in August, showed the average funeral costs £3,784.
Brady was given whole life sentences for the murders of John, Lesley Ann and Edward. Hindley was convicted of killing Lesley Ann and Edward and shielding Brady after John’s murder in being jailed for life. Both later confessed to the murders of Pauline, whose body was recovered in 1987, and Keith, whose body has never been found.