Suspects from genocides such as Rwanda are thought to be in the UK
Legal loopholes which allow foreign war criminals to escape prosecution in the UK should be closed, a report says.
The Aegis Trust says several people suspected of committing torture and genocide overseas, such as in Rwanda and Iraq, have entered the country.
The report also proposes strengthening the law on prosecuting suspects who are present in the UK.
A Ministry of Justice spokesman said tackling crimes of genocide requires international co-operation.
The Aegis Trust says it suspects alleged war criminals from Afghanistan, Sudan, Sierra Leone and Sri Lanka may be present in the UK.
They include a lieutenant colonel from the Soviet-era Afghan government's secret police, Khad, and an alleged Tamil Tiger assassination hit squad driver.
It's about individuals suspected of the most heinous crimes anyone can commit, individuals that this country needs to bring to justice if we do not want to remain a safe haven for war criminals
Nick Donovan, of the Aegis Trust
The report names Felicien Kabuga, accused of financing the Rwandan genocide, and Liberian Chucky Taylor, who was convicted of torture by the US, as two individuals who came to the UK but were not brought before the courts.
The Aegis Trust says the total number of suspects in the UK is not in the public domain.
Since 2004, the UK's Border Agency has screened 1,863 individuals for war crimes, genocide or crimes against humanity.
As a result, immigration action, which includes decisions to refuse entry, indefinite leave to remain and naturalisation, as well as exclusions from refugee protection, was taken against 138 people.
Since 2005 there have been 22 cases referred to the Metropolitan Police, but only one has resulted in successful prosecution, the report said.
The Human Rights Act prevents individuals being sent home if they could face torture or an unfair trial.
Mr Donovan is head of research, policy and campaigns for the Aegis Trust, which campaigns to prevent genocide worldwide.
He said there were two particular "impunity gaps" in UK law preventing prosecution for international crimes.
"Those suspected of genocide, crimes against humanity and most war crimes cannot be prosecuted in the UK if they committed those acts before 2001.
"And non-residents such as students, tourists or asylum seekers without residence status can't be prosecuted even if those acts were committed after 2001.
The report contains proposals for strengthening UK law, including proposed amendments to the International Criminal Court Act that would close the loopholes currently benefiting war crimes suspects in the UK.
Mr Donovan said Aegis Trust believes the law should be changed on residence "so as to apply to all those present in the UK, not just those resident here, thus extending it to those on student visas, business visas etc".
The Aegis Trust also wants the deadline for prosecutions for various crimes pushed back.
"We are calling for culpability for genocide to be moved back to 1948, crimes against humanity to 1991, grave breaches in international wars back to 1949 and war crimes in civil wars back to a variety of dates not earlier than 1945 and not later than 1998," Mr Donovan said.
A Ministry of Justice spokesman said: "The government will continue to work with other countries, including with the European Union, to ensure that criminal justice systems around the world are designed to deal with cases of this nature.
"However, as the justice secretary said on 5 May in the House, the all-party group on genocide prevention has made a very powerful case for the inclusion of genocide as an extra-territorial offence within British law."