"Totally on board with a crying baby being annoying but a friendly, 'Would you mind popping outside to see if baby quietens, you can leave your just purchased food here' would have sufficed. A little compassion goes a long way."
Mr Jackson, who runs the cafe along with his wife, said: "Parents have a responsibility to look after their children. We are a cafe, not a creche."
"We've had a number of complaints recently that our café is turning into a crèche. We don't have a policy about crying children but as business owners we are responsible for the overall environment.
"She was very politely asked if she would step outside for a minute to settle the baby but she chose to leave."
Another customer Dan Berrie complained on Instagram about the incident. He said: "Love what you guys do, but your attitude towards babies stinks.
"Our mate was asked to leave your place in East Dulwich today because her three month old was crying. Absolutely disgraceful kicking out (paying) customers for that reason. Hold your heads in shame."
The café responded: "If you have been to our cafe you would know that our attitude to babies does not stink. At any given time, there are a number of babies in the cafe. We provide high chairs, changing facilities, happily warm bottles and make babycinos and have no problem with breast feeding. But, we are a cafe not a crèche, and we have been getting an increasing number of complaints from (paying) customers about babies crying."
They added: "It's not something we relish or enjoy, quite to opposite in fact, but our goal is always to keep the majority of our customers happy and protect our business."