More than 3,500 reports of forced marriage were made to police over a three-year period, a Guardian investigation has found, as charities warned that there were thousands more victims living in conditions of modern slavery in homes across the UK.

Data shared exclusively with the Guardian revealed 3,546 reports between 2014 and 2016. But experts warn that the figures, collected by the Iranian and Kurdish Women’s Rights Organisation under the Freedom of Information Act, are just the tip of the iceberg.

Over the same three-year period, one national helpline run by another NGO received 22,030 calls from individuals or agencies concerned about a forced marriage. In 2017, the NGO Karma Nirvana received a further 8,870 calls, including more than 200 from or about children under 15, and gave advice regarding eight new clients under 10.

The new figures reveal the shocking extent of forced marriage in Britain – a crime that experts say should be investigated and prosecuted as a form of modern slavery.

They point to the fact that a guilty verdict last week against a mother who trafficked her daughter to be married in Pakistan was the first of its kind in the country despite the large number of reported offences.

Legal experts and campaigners say modern slavery legislation could lead to an increase in convictions for a crime that is notoriously hard to prosecute because victims are reluctant to testify against family members.

Last week’s landmark conviction resulted in a mother from Birmingham being jailed for four-and-a-half years for duping her 17-year-old daughter into travelling abroad and forcing her into marriage.

The woman had threatened to rip up her daughter’s passport if she did not marry the 34-year-old Pakistani national who had got her pregnant when she was just 13.

Karma Nirvana said the case was typical of reports it heard every week from those suffering domestic and sexual servitude within forced marriages.

Its director, Jasvinder Sanghera, said: “We know there are thousands of women and girls in Britain – but men, too – living behind closed doors in forced marriages, yet the crime is woefully under-reported.

“Treated as slaves and subjected to threats and violence, victims endure the added burden of their own families pressurising them to stay in these marriages to avoid bringing them shame.”

The majority of callers to its helpline are British citizens. Others have been brought to the UK by a British spouse before being exploited. Threatened with deportation, often unable to speak English and without access to public funds, they find themselves in a cycle of abuse.

A teenage girl confined to the house and raped on a daily basis; a Moroccan woman made to marry her gay British groom to conceal his sexuality and then used as a cleaner; and a West Yorkshire man coerced into handing over all his wages to his in-laws are among forced marriage victims who have contacted UK charities in recent months.

A leading barrister and adviser to the United Nations has warned the government is failing to recognise these people, and thousands like them, as requiring the same protection as those suffering other forms of exploitation.

Parosha Chandran said: “The modern-day meaning of slavery doesn’t require in law that you own somebody. Instead it means you treat someone as if they were your property. It’s crucial authorities acknowledge this in forced marriage cases.

“There has been no proper consideration in legal terms that a forced marriage involves elements of slavery – where a person is treated as if they are the property of the family they were married into.”

While forced marriage is among the acts prohibited under human trafficking EU law adopted by Britain in 2013, the legal provision has not translated to policy.

Referring to last week’s conviction, Chandran said: “This was also a human trafficking case with the girl taken abroad for the purposes of exploitation.

“Had the mother also been convicted under the Modern Slavery Act 2015, not only would she have faced a more severe penalty, but the judge should have considered ordering her to pay compensation to her daughter for effectively allowing her to be raped at 13 and forcing her to marry the perpetrator at 18.”

Forced marriage is not listed as an indicator of modern slavery under the national referral mechanism drawn up by the Home Office. Nor is there prosecuting guidance linking forced marriage and slavery crimes.

There have been just two convictions for forced marriage since it was criminalised in 2014. Last week’s conviction was the first to be secured after a victim gave evidence against a relative.

Chandran said: “Prosecuting guidance should include forced marriage among the exploitative purposes for which someone could be trafficked. Families who force their children to marry should know that is also a modern slavery offence carrying a sentence of up to life in prison.”

Mark Burns-Williamson, the national lead for human trafficking for the Association of Police and Crime Commissioners, agreed that a better understanding of the links between forced marriage and slavery was needed.

He said: “We are still working through the nuances of the Modern Slavery Act and how to apply the legislation to cases that could include forced marriage in order to secure the best outcomes at court.”

Victims of such crimes seldom recognise the abuse they suffer as unlawful because they have been groomed from a young age. Sanghera said: “Nowhere in their psyche do they own the abuse as a criminal offence. They are not thought of as slaves but if you have not consented to that marriage – you will be raped in that relationship – that is sexual slavery.

“And with victims moved between countries for the purpose of exploitation, the link with trafficking is clear.”

She said that although leaders including David Cameron and Theresa May had referred to forced marriage as a form of slavery, repeated calls to translate this into policy have been unsuccessful.

Sanghera added: “The crime has not been given the same spotlight as slavery but there remains a clear opportunity to raise the debate of forced marriage as part of the human trafficking agenda in the form of a national campaign.”

The national police lead for “honour” crime, commander Ivan Balhatchet, said: “It is unfortunate to hear repeated stories of newly-married women, often in forced marriages, complaining of a form of modern slavery. Undoubtedly, there needs to be much more awareness to detect and prevent these abuses.”

The Home Office said the government’s forced marriage unit provided support in almost 1,200 potential cases last year. Since its introduction in 2008, there have been more than 1,500 forced marriage protection orders issued. “This week’s forced marriage conviction shows that these appalling crimes do not have to be a hidden crime and, with the courage of victims, perpetrators will be prosecuted,” it added.