The boys – Leyton and Logan Hoath, aged three, and Kyson and Bryson Hoath, aged four – were killed after the fire on 16 December 2021.
Deveca Rose, 29, has been charged with child abandonment in addition to manslaughter, police say, and is expected to appear at Croydon Magistrates’ Court on Monday.
The children were treated at the scene before being taken to two south London hospitals where they were pronounced dead.
“They will be forever in my heart and thoughts, love Dad,” he said.
The Metropolitan Police said in a statement: “Officers understand the significant impact on the local community following this devastating incident, and they would like to reassure people that this extremely complex investigation continues, supported by partner agencies including the Crown Prosecution Service and London Fire Brigade.
“It is imperative that no material or comments are published or shared online that could prejudice future court proceedings.”