There is only a fleeting glance at this guest. Mr. Ingrams was checked in by Sybil half way through the Mr. Leeman fiasco. Originally we didn't even see him from the front, and his relevance was kept a tight mystery.
Later on, when Basil and Manuel are trying to hide Mr. Leeman's corpse, the two accidentally stumble into Mr. Ingram's room while he is blowing up an inflatable sex doll. Mr. Ingrams later appeared in the final scene where Basil promised that Sybil would give all the guests answers and explanations. Mr. Ingrams went to complain, probably due to the lack of privacy that he so obviously needed.
Mr. Ingrams existed as an in-joke: when the pilot episode A Touch of Class (the original name of Fawlty Towers) first aired it created many mixed reactions all around, some journalists believed it was a mediocre program, one of these being Richard Ingrams of the Private Eye, who slagged off the program with relish. After the show became a success, Cleese and Booth humiliated Ingrams, getting their revenge through this character.
Scene at 27:46