At Hampshire County Council's police and crime panel meeting in Winchester last week, Ms Jones answered concerns about the cost of the investigation into deaths at Gosport War Memorial Hospital between 1987 and 2001.
In June 2018, an independent panel report led by Bishop James Jones concluded that the patients all had their lives ‘shortened’ by the use of opioids at the hospital.
Representative for Gosport Borough Council, Cllr John Beavis MBE, said: ‘I mentioned to you at the financial working group some concerns over Operation Magenta, which is the investigation into the deaths at Gosport War Memorial Hospital.
‘The figure that’s being quoted that’s from your budget is £2m per year for a three-year period.
‘It's a significant amount of money - how will this affect your ability to deliver your police and crime plan?
‘You said you would be going to the Home Office to take this up with them.
'Do you think you'll be successful in your visit there in getting this charge taken away from your budget?'
Donna Jones replied: ‘In terms of whether I’ll be successful - if I’m honest it's unlikely, I put my chances at 40-50 per cent at best because ultimately it’s me versus the Treasury.
‘If this was a national publicly-ordered inquiry such as Hillsborough this would have a different funding package - but this is being treated as a murder investigation and therefore the responsibility falls upon the chief constable.
‘That £2m that we are paying is only 40 per cent of the cost, with most coming from Home Office grants due to the significance of this being Britain's largest murder investigation - I don’t want to use evocative words but it potentially is, if we get to where we think we will with the number of victims identified.
'It's huge. It's an incredibly large investigation, with more than 100 investigators working on Operation Magenta.
'It's disgraceful and appalling, and the sheer volume of criminality that I think is coming out of the investigation is horrendous. What's more, we could be waiting another three to four years.'
David Wilson's aunt, 86-year-old Dulcie Middleton, died in 2001 after being transferred from the hospital.
Her death is one of four inquests opened by the coroner, which were applied for by solicitors Leigh Day, which described the investigations as ‘ineffective’.
Mr Wilson, 75, is critical of the commissioner's office 'looking elsewhere' for the costs to be covered.
He said: 'At the end of the day, it's still the taxpayer who is paying the price for this, and they have done so for far too many years.
‘The investigation by Operation Magenta is a shambles. Many of us have no trust or confidence in it.
‘Many will be pleased to see Mrs Jones describe this as a “murder investigation” and she's right about the criminality that we've seen, but as for waiting another three or four years - well, that's what Operation Magenta thinks anyway.’
Responding to Mrs Jones’ comments, deputy assistant commissioner Neil Jerome, from Operation Magenta, explained that 150 people are currently working on the case and a 'full range' of criminal offences are being examined, including homicides.
He said: 'The investigation is progressing well with officers and staff continuing to take witness statements and reviewing millions of pages of documents relating to more than 700 patients.’
The Home Office said that the Hampshire Police and Crime Commissioner has received £5.3m of funding from the Police Special Grant since Operation Magenta began.
Government ministers have also agreed to provide up to £6.5m of further funding in 2021-22. Both the Home Office and police and crime commissioner’s oiffice were asked how many years of the investigation this money would cover, but did not respond.