The officer met a 16-year-old girl while he was on-duty in Brent dealing with a domestic case.
He then drove her to a nature reserve while off-duty under the pretext of taking a statement and asked to kiss her.
On another occasion he drove her to a car park where he kissed her and touched her thigh and waist, a court heard.
Homersham, from Southgate, later texted her and said he was going to pick her up from school and have sex with her.
He later admitted a charge of misconduct in public office.
Laurence Taylor, Assistant Commissioner for Professionalism, said: “Former PC Homersham acted intentionally in taking advantage of his position in having an inappropriate relationship with a 16 year old girl whom he met during his work as an officer, resulting in a conviction for misconduct in public office.”
He decided that had Homersham not already resigned, he would have been dismissed.
