Gracie, 23, was found fatally injured in Duckmanton on June 18.
It is understood she was killed by 35-year-old Michael Sellers, whose body was also discovered that day.
The Independent Office for Police Conduct (IOPC) is investigating Derbyshire Constabulary following Gracie's death – and the watchdog released a statement on Friday which included news that five police officers were served with disciplinary notices.
Chesterfield MP Toby Perkins said he shared the concerns of Gracie’s family.
“The IOPC are clearly taking this investigation very seriously and I am grateful for their update and confirmation of the actions taken so far,” Mr Perkins said.
“I met with the IOPC and discussed their protocols and the way that they would handle this investigation and discussed some of my concerns.
“I would not want to pre-empt the outcome of the investigation whilst it is ongoing, but share the view of the family that there is significant cause for concern about the steps that could have been taken to keep Gracie safe and weren’t by Derbyshire Police.
“The circumstances regarding the bag that was found close to where Gracie was murdered several weeks later are very troubling and the issuing of a gross misconduct to a sergeant and misconduct notices to two constables is testament to gravity of the concerns raised and the seriousness of the IOPC investigation into police failures.
“I have had conversations with senior police officers regarding Gracie’s case and a number of other cases that have been brought to my attention regarding, the police response to allegations of stalking and harassment. I am assured that there have been measures taken to change the culture within the force, as well as practical steps taken to improve the investigation of these crimes.
“I would still urge people to sign the petition for Gracie’s Law, which is calling for the Government to provide more funding for stalking advocates for victims of stalking. The petition currently has just over 81,000 signatures and if it reaches 100,000 will be debated in Parliament.
“You can the petition at https://petition.parliament.uk/petitions/593769”