Alan Borg, the museum's director, said yesterday that police were examining all options. He added: "We are obviously extremely concerned about this, and we want them back. The sketches weren't on display at the time of the loss, but it goes without saying that all Constables are important."
The two oil sketches are Dedham Lock and Mill (1810) and Sketch for `The Valley Farm' (1835), valued at pounds 500,000 and pounds 300,000.
Timothy Stevens, assistant director of collections, said that during a check it was discovered that the two sketches were not in their correct storage locations. "After a comprehensive search by V & A staff through the million works held by the prints, drawing and paintings department, the works were not found, and have formally been declared missing."
Mr Stevens said the Dedham Lock and Mill sketch was particularly important to the museum as the V & A has the finished picture as well and "you can see how Constable adjusted what was really there into the picture, how he adjusted reality".
Staff at the museum have spent the past week sifting through the collections to try to find the missing works.
The sketches were part of a group audited in August. Mr Stevens said it had been concluded from this that "theft has therefore been identified as the most likely cause. The police and the Art Loss register have been notified."
The last major art loss at the V & A was in 1992, when the 16th-century Medici Casket went missing. It was returned to the museum after extensive publicity.