In its letter, the Independent Monitoring Board (IMB) raised specific concerns about the “evidently ready availability” of psychoactive substances such as spice and the “caustic impact” this was having on the prison population and staff.
Child killer Deane, 22, was murdered by cellmate John Westland on November 12 last year while serving a life sentence.
Jurors heard how the pair would take spice – a synthetic cannabinoid – in their cell “every day”.
The IMB’s latest annual report highlights that there were three deaths in custody at Leeds during 2017 and at least one incident reported involving psychoactive substances on “virtually every day of the reporting year together with frequent and sustained instances of violence”.
It said the number of serious incidents related to psychoactive substances rose from an average of 3.9 per week between May and August 2015 to eight per week in the same period in 2017.
The report said: “The amount of drugs, particularly psychoactive substances, entering the prison on a virtually continual basis was worrying, but the IMB applauds the varied actions taken to try and reduce supply.
"These included officer patrols round the perimeter of the prison, increased use of dogs, personnel searches and targeted cell searches. The latter were particularly successful.”
In its letter, the IMB suggested there were four “very serious” inter-related issues facing the prison that merit Ministerial attention and specific action.
These were staffing levels, the ageing Victorian buildings of the prison in Armley, illicit drugs and mobile telephones, and inadequate access to health and social care.
A response from the Minister in mid-January simply acknowledged that the issues had been raised, something the IMB expressed disappointment about in its report.
It wrote: "The IMB was deeply worried that the response to its letter merely acknowledged what were profound concerns of the Board and the Minister’s response implied that everything
was “under control”.
"In this report the IMB raises the same concerns again and highlights the similar issues and concerns raised by HM Inspectorate of Prisons.
"The IMB invites the Minister to provide a full and considered public response as to how the situation can be improved both in the immediate term but, as importantly, in the longer term with specific targets and standards to be achieved in a timeline with defined milestones."
The report itself, published in April, is also yet to receive a full response from the Minister.
A Prison Service spokesman said: “This inspection finished in December 2017 and a number of improvements have been made since then.
“We are providing staff with new suicide training and have strengthened the monitoring of prisoners at risk of self-harm.
“The best way to keep staff and inmates safe is to keep drugs out of our prisons. That is why have created a new drugs taskforce, trained over 300 sniffer dogs and are rolling out new body scanners to tackle the supply and use of drugs across the estate.”