The 17-year-old boys, who were on a school trip, were spotted acting suspiciously at the Auschwitz-Birkenau State Museum in southern Poland and were held at the police headquarters in Oswiecim until yesterday.
Polish police said the boys denied any wrongdoing, and were spared a fine because they are “not working”.
Had they been found guilty of theft the boys could have been jailed for 10 years.
Police said the pair were found with fragments of hair clippers, spoons, buttons, and two pieces of glass after they were apprehended in warehouse number five — known as Canada — where the belongings of Auschwitz arrivals were seized during the Holocaust.
The Holocaust Educational Trust’s CEO Karen Pollock said:
“We have a duty to educate the next generation to prevent ignorance and hate, and in over 15 years of organising for thousands of British teenagers to visit Auschwitz-Birkenau, we have never known of such an incident.
"We would gladly work with these young boys to ensure they understand the implications of their actions although this is now a matter for the police.”
A Foreign Office spokeswoman said: “We are in contact with the Polish authorities and stand ready to provide consular assistance.”
Visitors have tried to steal artefacts as souvenirs from the museum in the past.