I am directly related to William Faichen who was born in 1780/90 ish. I believe his father was a publican in Portsmouth. According to the book 'The Annals of Old ropley" (you can Google it as it is on the net) He ran away from his father's pub in Portsmouth. I believe samuel ran a pub in Medstead before going to Portsmaouth, and there are Faichen baptisms in that church - but not for my William ( not sure about your Ann).
It may be worth looking at them to see if she is there.
Hope this helps
Alice