Ian Brown, 44, and Daniel Dunkley, 35, died following incidents in their cells at HMP Woodhill last July.
Their relatives claim Woodhill's governor has not complied fully with Prison Service Instructions (PSIs).
But the governor and the Secretary of State say the judicial review claim is "neither appropriate or necessary".
PSIs cover management of prisoners at risk of harm to self, others and from others, early days in custody and medical emergency response codes.
Heather Williams QC, for the families, said the claim addressed the "exceptionally high" rate of self-inflicted deaths at the Milton Keynes prison.
There were seven self-inflicted deaths last year, five in 2015 and 18 at the prison since May 2013.
"The rate of self-inflicted death at HMP Woodhill is far higher than at any other prison, at a time when the suicide rate in the prison estate as a whole is at a record high," said Ms Williams.
She said the case raised serious ongoing breaches of Article 2 of the Human Rights Act, which protects the right to life, and involved long-term failures to comply with the responsibility placed on the authorities to protect prisoners.
James Strachan QC said the governor was well aware of his obligations to comply with the requirements of the PSIs.
"The defendants do not dispute that the number of deaths at the prison is a legitimate matter of concern.
"However, not only have the governor and the Secretary of State taken significant action in 2016 to improve the situation, but as the taskforce approach shows, this is a continuing high priority."
Lord Justice Irwin and Mr Justice Garnham will give their decision at a later date.
Families of two men who died in prison have brought a High Court case over the "exceptionally" high rate of self-inflicted deaths there.