A man, aged 46, and a woman, aged 23, have been arrested on suspicion of fraud and the prevention of a lawful and decent burial.
Concerns were first raised on Wednesday when police received a report from a member of the public about the storage and management processes relating to the “care of the deceased”.
The funeral home, on Hessle Road, was closed while officers carried out enquiries and a number of bodies were subsequently removed from the site.
In a statement on Sunday afternoon, Humberside Police said that 34 deceased people have now been transported from the funeral home to the Hull mortuary for formal identification to take place.
The suspects have been arrested on suspicion of fraud by false representation and fraud by abuse of position and remained in police custody on Sunday.
Police cordons remain in place at all three Legacy Independent Funeral Directors: two in Hull and one in Beverley, also in East Yorkshire.
A dedicated phone line was set up on Friday and officers have since received more than 350 phone calls from concerned members of the public.
Officers are working with local councils and the coroner.
Humberside Police also said victim support also has a dedicated telephone line which is available to anyone who is experiencing distress or concern following this report and would like advice and guidance. The number is 0808 16 89 111.