[2] He joined a social democratic student organization, Frit Forum, during his studies at the university.
[1] The same year he resigned from his job as headmaster and began to involve in politics being a member of the Social Democrats.
[4][9] Heinesen was appointed minister of budget 27 September 1973, replacing Per Hækkerup in the post.
[1][10][11][12] Heinesen resigned from office in 1979 and was succeeded by Svend Jakobsen, but he served as the vice president of the Social Democrats.
[4][13] Heinesen was named as the minister of public works on 15 October 1981 when Jens Risgaard Knudsen had to resign from the office due to his involvement in a scandal.