Students who cheated during exams by seeing the papers beforehand have been identified, school authorities say.
Thousands of students sat the biology exam on Friday
The papers appear to have been stolen from a north London college in two separate break-ins over three days.
A-level papers set by Edexcel were reported stolen on 11 June and 14 June, before being leaked to a newspaper and apparently offered for sale.
Edexcel said: "We knew which papers [were stolen], we knew where and we are already catching cheats."
The Qualifications and Curriculum Authority (QCA) said it was aware of "a localised security breach involving more than one awarding body."
A spokesman for the Met police said they had been notified of exam paper theft from a college on two occasions, but could not confirm whether they related to separate crimes.
A QCA spokeswoman added: "The thousands of pupils who have already sat and are still taking their exams can have confidence that this is a localised incident and that they will receive the grades they deserve."
Students sat a biology exam on Friday despite the fact a copy was leaked to the Daily Telegraph by a student.
Another newspaper had already been passed maths and chemistry papers, questions from one of which were posted on the internet.
Three schools in north-west London have reported papers for sale and it is thought at least five individual papers, stored in a locked store, have been leaked.
Exam board Edexcel says it knew A-level papers had been stolen 11 days before students were due to sit the tests, but it was too late to change the biology exam.
"We reported the papers stolen on 14 June. We decided in consultation with the QCA that the exams should go ahead."
It is to "substantially change" one of the chemistry exams, due to be sat on Tuesday and says it removed all its exam papers from the unnamed college in Harrow on 14 June.
On Friday Edexcel said examiners had already found "irregularities indicating cheating" on some students' papers and would withhold grades while police investigations continued.
It is the second time in three years Edexcel papers have been found on sale.
No system safe
Chris Keates, of the NASUWT teaching union, said the exam board needed to have a thorough investigation into its own procedures.
She told BBC Radio 4's Today programme: "Edexcel year on year appears to be accident-prone, particularly this year, with a number of scares about leaked papers.
"Clearly they can't be blamed if the leak has been at a school or college level, and no system is 100% safe.
"But one of the problems with Edexcel is that, unlike the other awarding bodies, they don't actually work constructively with the trade unions to look at all the issues involved in making sure we have a safe, secure and transparent system."
Edexcel says it hopes criminal charges will follow the police inquiry.