At the Queen's Speech debate, The Bishop of Peterborough, Rt Revd Donald Allister, said it was "perplexing" that the government did not propose a new bill.
According to the BBC, he said he hopes the aim included in the Queen's Speech of improving mental health results in "not just money but deliverability and accountability".
He added that leaving the NHS in charge of mental health strategy "isn't good enough".
He continued: "We have a national health service and the government must be in charge of it, it must take responsibility not fob it off onto others."
Her Majesty the Queen said in her speech last week: "My government will reform mental health legislation and ensure that mental health is prioritised in the National Health Service in England."
Bishop Donald's speech come as new figures show the number of prescriptions handed out for anti-depressants is at an all-time high.
According to data from NHS Digital, prescriptions for the drugs across England rose by 3.7 million items in 2016, from 61 million to 64.7 million.
This means the number of anti-depressant prescriptions has more than doubled in the last decade - in 2006 there were 31 million such prescriptions.
Dr Kate Lovett, dean of the Royal College of Psychiatrists, said: "For many milder episodes of depression, talking therapies will be recommended as the first line.
"However, there is evidence that for people who have recurrent episodes of depression longer use of anti-depressants reduces incidence of relapse and in certain situations this will be clinically appropriate."
