The verse that you are quoting is part of Thompson's longest poem, named Sister Songs, completed in 1896. I have read variations of the story of how Thompson and his prostitute met, including this one in which he was rescued, from a pedestrian accident. I know that Thompson was struck by a cab, in his later years, after the murders and sustained a head injury. My feeling is that he used that experience in Sister Songs as a metaphor for the life sustaining assistance his prostitute gave him.
The sources of when Thompson first met his prostitute and when they breakup occurred, are derived ultimately from Thompson, but several books, place the time-frame as meeting in June of 1887 and parting June of 1888. The Life of Francis Thompson, 1913 edition, by Everard Meynell is a good book to read. It was written by the son of his editor and the son knew Thompson for many years.
Thanks for showing an interest jerryd.