Terry McMillan, 58, and Brendan McMillan, 27, of Chislehurst, died after the alleged incident at their family business in Long Lane, Bermondsey, on July 28.
Hassan Cevik, 31, appeared at the Old Bailey via video link on Wednesday charged with two counts of murder.
Cevik, of Mount Pleasant Lane in Hackney, is also charged with grievous bodily harm relating to a 47-year-old man and possession of an offensive weapon.
The Metropolitan Police were called to the commercial property in the Southwark district on July 28 after reports of multiple stabbings.
Two other men were treated for stab wounds by emergency services and taken to hospital.
Cevik was arrested and also taken to hospital.
The defendant, who currently uses a wheelchair, was ordered to next appear for a preliminary hearing at