Mr. O'Reilly was an ineffective and God-fearing Irish builder played by actor David Kelly who Basil hires in The Builders. His shoddy workmanship and complete lack of knowledge in the field of building works almost resulted in the Fawlty Towers hotel collapsing.
In the episode, Basil and Sybil are going away for the weekend and want some foundation work done on the hotel during their absence. Sybil sensibly decides to use professional builders, but foolishly lets Basil oversee everything. Not wanting a huge bill to pay, Basil hires O'Reilly. O'Reilly and his men are totally incompetent cowboys, but Basil frequently uses him because he's cheap. Sybil mentions that O'Reilly has worked for them three times in the past year and every time, it has been a catastrophe. O'Reilly was called in to build a garden wall and simply left the huge pile of bricks in the driveway instead of actually building it. He also attempted to change a washer in the hotel, resulting in the hotel having no running water for two weeks. Sybil abhors O'Reilly, which is totally understandable and attacked him after he dared to smile cheerily at her when she was viciously insulting him about how completely useless he was.
O'Reilly is the only character, other than Basil himself, who gets to be on the receiving end of Sybil's wrath. He is also one of the very few guest characters to receive a mention in more than one episode: we see Basil complaining to him over the phone, about the garden wall, in A Touch of Class. Memorably, Sybil noted that she had seen more intelligent creatures than O'Reilly lying on their backs at the bottom of ponds. She then hit him several times with an umbrella.
Basil convinced O'Reilly into doing the best day's work he'd ever done. The hotel looked faultless after O'Reilly had worked upon it, however rival builder Mr. Stubbs realized that the supporting walls were in fact in danger of falling down because of the incorrect usage of materials, leaving the Fawltys in a complete crisis.
Basil then stormed away, vowing to insert a large garden gnome in O'Reilly's behind.