Abram, 34, was cleared of attempted murder of Harrison and his wife.
They spoke out ahead of Health Secretary Alan Milburn's unveiling of significant changes to the legislation this week.
One of the key proposals contained in a government White Paper would allow victims to be told when their attackers are released from mental institutions.
George and Olivia Harrison, who underwent a knife ordeal at the hands of an insane man in their home a year ago, welcomed the reforms.
They wrote: "Since the attack, we have had a number of letters - both from people revealing horrendous attacks on them or their children by mentally ill people who have been released too early from mental hospitals, as well as parents of paranoid schizophrenics who have been treated with shameful inadequacy.
"There clearly need to be much stricter criteria applied and although it is impossible to generalise, clearly major mistakes are being made regularly with devastating results, as in our case."
Independent inquiry
Michael Abram was sent indefinitely to a secure psychiatric hospital last month for attacking the Harrisons at their home in Henley-on-Thames.
An independent inquiry is being held to examine Abram's medical history.
There has been criticism of doctors at a Liverpool hospital who allegedly mistook Abram's mental illness for drug addiction.
Abram, 34, was cleared of attempted murder of Harrison and his wife.
He stabbed the musician 10 times in a frenzied attack on 30 December 1999.
The Harrisons' letter to the newspaper raises failures in the way Britain deals with those who are dangerously mentally ill and their victims.
They say that case law and human rights legislation lay down a positive duty on the state to protect those whose lives may be at risk by the criminal acts of others.
The White Paper is also expected to include the introduction of community treatment orders which force patients to comply wth their treatment after they have been released into care in the community.