Draper said children will still be welcome to Sunday lunch with their family.
She said she was forced to make the controversial policy after an increase in badly behaved children visiting her venue.
"It's their parents' fault," she told the Sun.
"They just don't discipline them, so 75 per cent of the children that come in now, they're screaming and running around and not sitting at tables.
"Families will come in here around 5pm after their children have been in the park all day long and they're hyper. They should be taken home to bed.
"The other day I had to move two tables out of one of our rooms because there was a family in there with four children and they couldn't hear themselves think.
"This pub is an adult environment. It shouldn't be a children's creche and most of my regulars are there every day or two to three times per week just for a quiet drink or meal.
"It's a great shame I've had to do it for some people, because we get quite a few nice children." Draper's pub, which employs 12 staff, has three small rooms and can seat up to 35 people. An extra 35 patrons can be seated in the garden area.
"From today, September 1, we are predominantly an adult-only premises," the announcement read.
"Children over 12 are permitted to dine on any date at any time, but children under 12 are only permitted at our 12pm and 2.30pm sittings."
Some social media users jumped to Draper's defence, agreeing that a pub is an adult environment that many visit for peace and quiet of an afternoon.
"It's lovely to have somewhere that adults can have a relaxing meal," one person wrote.
"Not everyone wants to go to a pub with children. It's nice to have somewhere relaxing to go."
"We need more mostly adults only places, it's nice to know poorly behaved kids won't be ruining our meal," another added.