Staff at the independent Harrow Park tutorial college alerted police to the theft from a locked store at the site on June 11.
Examining bodies Edexcel, Assessment and Qualifications Alliance (AQA) and Oxford Cambridge and RSA Examinations (OCR) had 24 GCSE, AS-level and A-level question papers stolen.
As a result Edexcel on Tuesday changed part of its chemistry A-level, which around 8,000 students sat, while AQA changed two of the five papers it lost, but declined to say which ones.
Students in the area are alleged to have been offered the papers for between pound;300 and pound;1,000. On June 20 two questions from a pure maths A-level appeared on the internet a day before students sat the exam.
In another incident the Daily Mirror handed Edexcel pages from four A-level maths and chemistry papers it is thought to have obtained from a student.
Edexcel said several cheats had been identified and their grades would be withheld pending further inquiries.
A spokeswoman said: "A small number of students have been allowed to cheat.
Clearly this is an horrendous breach of trust and we hope that, on conclusion of the police inquiry, criminal charges will follow."
An AQA spokeswoman said: "We have replaced two papers and the three we did not will be subject to stringent checks. Those found to have cheated are risking their futures. They could be banned from taking exams for a number of years."
The majority of OCR's 24 stolen papers were taken by students without any changes being made.
A spokesman said: "It would have been logistically impossible to replace the papers. OCR is closely investigating all the papers from the centre where the security breach has taken place. We are confident we will identify any cheating and indeed have already identified individuals against whom we will be taking action."
A spokesman for the exams watchdog, the Qualifications and Curriculum Authority, said: "It is an option to swap papers, but it means withdrawing them from every centre and issuing new ones. This is a localised problem so we are able to monitor the centre's performance closely."