In Family Guy S10E22 "Family Guy Viewer Mail #2", Brian says that Family Guy is based on an English show named "Chap of the Manor".
Ιs there actually a show that resembles that?
Wikipedia doesn't have any insight.
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That Wiki link actually has a lot of insight. The first line in the plot section:
The episode uses the premise that Family Guy is based on a British television show.
Premise being the key word.
In the Cultural References section:
In the interlude to the Chap of the Manor segment, Stewie jokingly says that Family Guy is based on The Simpsons, another animated comedy series, but later claims it is based on a British television show, like the TV series The Office.
The reference to The Simpsons should give you an indication that the tongue is firmly planted in cheek.
The Chap of the Manor segment featured references to the classic British series Benny Hill (manic, sped up chase sequence between Peter, Chris and the coppers), sketch show Monty Python's Flying Circus (jump cut to footage of old dowagers clapping & laughing in the cutaway gag), and Fawlty Towers (letter R falling off of the word "Manor" in the title sequence).
Too many obvious references to other famous British shows.
Putting all of this information together, it's pretty obvious that Chap Of The Manor is fictional.