An independent review into the welfare of immigration detainees commissioned by the home secretary has called for ministers to reduce “boldly and without delay” the 30,000 people detained each year.

The report by Stephen Shaw, the former prisons and probation ombudsman, calls for a complete ban on the detention of pregnant women in immigration centres such as Yarl’s Wood. He says there should also be a “presumption against detention” of victims of rape and sexual violence, people with learning difficulties, and those with post-traumatic stress disorder.

The six-month review was commissioned by the home secretary, Theresa May, after years of criticism about the treatment of immigration detainees including incidents of deaths, self-harm and sexual abuse in Britain’s 10 immigration removal centres.

May tried to exclude any consideration of introducing a statutory time limit on the use of immigration detention, but Shaw makes clear his belief that the numbers should be reduced “both for reasons of welfare and to deliver better use of public money”.

In a particularly damning finding, the report says that despite the rapid growth in the use of immigration detention in Britain – where 3,000 people are locked up at any given time and 30,000 pass through the system each year – there is no correlation between the number of people detained and the number of people lawfully deported.

His report also highlights medical research showing that immigration detention itself can seriously damage the mental health of detainees. Shaw concludes that this finding has “evident ethical, policy and practical implications”, and stresses the importance of curbing excessive periods of detention.

He calls for rule 35, which is designed to screen torture victims out from detention, to be immediately scrapped due to strong evidence that it is not working, and for the closure of the Cedars centre near Gatwick, where children are detained with their families.

“There is too much detention; detention is not a particularly effective means of ensuring that those with no right to remain do in fact leave the UK; and many practices and processes associated with detention are in urgent need of reform,” Shaw says in his conclusions.

“Most of those currently in detention do not represent a serious [or any] risk to the public, and many represent a very low risk of noncompliance because of their strong domestic links to the UK,” says Shaw, suggesting that a combination of tagging, residence and reporting restrictions, and promoting voluntary returns could be used instead.

The Refugee Council welcomed the Shaw report, saying he had shone a spotlight on the hidden, abhorrent and often unlawful treatment of vulnerable people inside Britain’s shadowy immigration estate. Campaign group Freedom from Torture described it as a “stunning indictment” of immigration detention, and said he had vindicated their concerns about the operation of rule 35 doctors’ reports.

Shaw’s report was delivered to the home secretary in September but only published on Thursday. The immigration minister, James Brokenshire, accepted that there should be a presumption against detention for a new category of “adults at risk”, including sexual violence victims. However he stopped short of implementing an outright ban on the detention of pregnant women called for in the report.

Brokenshire said immigration officials would respond to Shaw’s concerns about the mental health of detainees by carrying out more detailed mental health needs assessments.

The minister also announced a new drive to minimise the time detainees spend locked up before they leave the country “without the potential abuse of the system that arbitrary time limits could create”.

“The government expects these reforms, and broader changes in legislation and policy to lead to a reduction of in the number of those detained, and the duration of detention before removal,” said Brokenshire.

The Shaw report is be followed by a fresh cross-party attempt to amend the current immigration bill to include a statutory 28-day time limit on the use of immigration detention.