Prison reformers have called for more support for new inmates in order to prevent suicides.
The first few nights in jail are the worst for new inmates
The Prison Reform Trust says providing free phone calls to family or friends would reduce stress amongst prisoners during their first few nights in jail.
Research by the trust indicates that almost a third of suicides occur within the first week of imprisonment.
It says that most prisoners are more worried about life outside jail, rather than what will happen to them inside.
The director of the Prison Reform Trust, Juliet Lyon, said: "A simple phone call to family may make all the difference in stopping a new prisoner feeling completely overwhelmed by fears and uncertainties."
A report by the trust calls for all prisons to follow the example of Exeter, Holloway and Wandsworth prisons, all of which have "first night" services designed to minimise prisoner stress.
New prisoners are interviewed, and if necessary referred to specialist services. They are also given the opportunity to make phone calls to let their families know they are safe.
The report: There When You Need Them Most, says that these measures can play a "key role" in reducing the stress experienced by prisoners.
The authors interviewed 91 prisoners in six prisons and asked them what they were most worried about when they entered jail.
Two-thirds of those interviewed said they were worried about their families. In particular, prisoners are anxious to let their families know their whereabouts.
One prisoner told the report's authors of the difficulty he has had in contacting his elderly and frail parents. He said: "I can't find a way to tell them I am in prison.
"I was thinking of writing them a letter, but how can I put it? So that has been a big worry. They said I had a free phone call. I said I didn't want it then.
"They said: 'Well, you can come get it within a week.' I went back and they said 'You're too late. You'll have to pay for it yourself.' But I have no money."
The trust also blames much of the stress inmates suffer on the current record-high prison population.
Ms Lyon said: "No one knows how many more first nights people will have to endure as they are bussed from one overcrowded jail to another as the prison system tries to cope with the growing number of people in prison.