Makers of the HBO drama series, which is about racing horses, were last month accused by animal rights group Peta of cruelty, when two animals were injured during filming of the first series, in 2010 and 2011.

A third horse died while filming the second series in California, after rearing up and falling back. The horse had to be put down because the injuries were so severe.

The series is Hoffman’s debut TV appearance.

The American Humane Association (AHA), which was not informed of the deaths until after filming, has now demanded “that all production involving horses shut down” while an investigation takes place.

HBO said in a statement that an AHA safety representative was at the track when the third accident occurred and “as always, all safety precautions were in place”.

Peta vice president, Kathey Guillermo, is pushing for stricter safety guidelines for TV and film crews, after suggesting the horses on Luck were not treated properly on set.

She said: “Three horses have now died and all the evidence we have gathered points to sloppy oversight, the use of unfit, injured horses, and disregard for the treatment of thoroughbreds.”