The chicks were found sitting in their nest by driver Barry Dalton as he was doing a safety check on the vehicle.
Four chicks were found, although one named John, has since died.
Secret World Wildlife Rescue centre named the surviving chicks Paul, George and Ringo after The Beatles and will release them into the wild.
Mr Dalton said: "Sometimes we find old nests in our vehicles but we've never found a nest full of baby birds before."
Three robin chicks have survived a 192-mile (309km) road trip from Liverpool to Glastonbury on the chassis of a trailer.