LONDON—A U.K. regulator on Monday gave the green light to scientists to genetically modify human embryos as part of fertility research, putting Britain on course to be among the first countries to approve an experiment with the controversial genome-editing technique.

The decision by the independent regulator on fertility treatment and embryo research is a major step to allowing scientists to use the technique, known as CRISPR-Cas9. The technique has generated excitement as a way to possibly replace defective genes and eradicate...