There are now five applicants for every vacancy in the industry in England, according to the study by ConstructionSkills, the skills council for the building sector.
More than 12,000 candidates have applied for a job this year but only 2,400 vacancies have been offered by employers, said the report.
ConstructionSkills director of apprentices Max Hamps said: "There are hundreds of thousands of construction firms in England but only a fraction of these are taking on apprentices. The small businesses that thrive from generation to generation are those that appreciate the value of training and bringing young people into the business from day one.
"Unfortunately many firms still think that taking on an apprentice is costly or time consuming, or that drop out rates are high. In fact with over 75 per cent completion rates ConstructionSkills apprentices are among the best in the industry and we are committed to finding the right apprentice to suit each construction business."