"During my time at the FA I was sexually harassed by David Davies," she told the tribunal.
"I was subjected to Mr Davies's unwelcome attentions." She added that Davies "had a bit of a reputation".
Two women colleagues had told her that Davies had "tried it on with them", she said.
Davies denied the allegations in a statement, saying they would be "refuted vehemently."
Alam, 39, had an affair with both England coach Sven-Goran Eriksson and the FA's chief executive Mark Palios. Palios resigned in mid-2004 after the affairs became public.
Alam resigned shortly after Palios and is suing the game's ruling body in England for alleged sexual harassment, unfair dismissal and breach of contract.
Alam said Davies had told her he wanted to "lock her up and throw away the key." She also told the tribunal he had tried to hold her and had kissed and hugged her.
"In October 2002 at his flat he tried to hold me close and kiss me. When I left he managed to kiss me on the lips," she said.
"He attempted to hug me in his office and put his arms round me. Alone in a lift together he would try to kiss me on the lips.
"I would rebuff him. He advised me that his life was better with me in it and said that we should run away together. He said he wanted to lock me up and throw away the key."
It triggered the resignations of Palios and Colin Gibson, the FA's then director of communications, after he tried unsuccessfully to broker a deal to keep details of Palios's affair, but not Eriksson's, out of the papers.
As for her decision to leave the FA, Alam said on Tuesday: "I felt let down by the FA and humiliated. It appeared that the FA was prepared to sell Mr Eriksson and me down the river in order to protect Mr Palios," she said.
"I was horrified that the FA was prepared to treat me in such a shabby manner. I did not see how I could possibly go back there."