The parents of murdered six-year-old Ellie Butler have appeared via video link from their respective prisons at an inquest hearing into the death of their daughter, and interrupted the proceedings several times.

Many at the inquest, including Neal Gray, grandfather of Ellie who was murdered by her father, appeared surprised that Ben Butler and Jennie Gray were participating in the proceedings.

Both parents said they were in the process of appealing against their convictions. They asked a series of questions of retired high court judge Linda Dobbs, who has taken over the inquest from senior south London coroner Selena Lynch.

Gray said she would like to challenge submissions her father, Neal, would be making to have the inquest heard in front of a jury.

“Would I also be able to challenge those submissions about whether it’s a judge or a jury?” she asked.

She added that she wanted the inquest to explore medical factors and cause of Ellie’s death but had seen an email that suggested these issues would not be part of the inquest’s remit.

“I’m coming at this from a layperson’s point of view,” said Butler. “There are questions I want to ask you that I don’t know if I’m able to ask you.”

Dobbs urged both parents to apply for legal aid so they could be represented at the inquest.

Dobbs said the full inquest would be article 2 compliant, meaning the role of the state in Ellie’s death would be examined.

“Were there failures on the part of the authorities, agencies and individuals to protect Ellie’s life and prevent her death?” said Dobbs.

Lynch was originally going to preside over the inquest but because of the complexity of the case and the issues of wider importance raised by the girl’s murder, Lynch referred the case to the chief coroner. After discussions with the lord chief justice and the lord chancellor it was agreed that Dobbs should take over.

Dobbs said: “This has been postponed for a long time. I’m very keen in the interests of everyone that this inquest be determined as soon as possible.”

Dame Mary Hogg, the now retired family court judge who ruled that Ellie should be returned to her father, who subsequently murdered her, could be required to give evidence. At a hearing last November at Croydon coroner’s court into whether to reopen the inquest into the death, Lynch said the role the family court played in Ellie’s case was key and that Hogg could be asked to attend.

She added that any investigation of the judiciary raised constitutional issues and highlighted the difficulty of a more junior court investigating a higher one.

“How can I investigate a superior court?” Lynch asked.

At the November hearing Lynch added that the scope of the inquest would be wide ranging. As well as engaging with the family court she requested evidence from the social workers at Sutton council, the independent social workers from Services for Children (S4C) who supervised Ellie’s return to her parents, the two schools the child attended, her paediatrician, her GP and the two hospitals (Chelsea and Westminster and St Helier) Jennie Gray attended after violence from Ben Butler.

James Elliott of Wilsons Solicitors, which is representing Neal Gray at the inquest, said: “Mr Gray and his legal team are very pleased that Ellie’s inquest is now moving forward. We hope that the timetable set out at today’s hearing will enable the coroner to get to the truth of what happened to Ellie and to be able to make recommendations to ensure no family has to go through this again.”

Neal Gray donated money to Ellie’s old school, Avenue primary academy. One of the things the school has used the money for is to buy and name a trophy in Ellie’s name – the Ellie Butler award for creativity, given to a year six pupil each year.

Ben Butler was jailed for life with a minimum term of 23 years in June 2016 for murdering Ellie. Jennie Gray was sentenced to 42 months for child cruelty and attempting to pervert the course of justice.