Corporation rangers caught the dog, a Staffordshire bull terrier, just after the attack on the herd on 8 May last year. One Jacob sheep had to be put down after the mauling.
Peter Kelly of Purley pleaded guilty to failing to keep his dog under control, contrary to byelaw 2(24) of the Coulsdon Commons Byelaws, at Croydon Magistrates Court on 21 January.
Corporation head ranger at Riddlesdown Common Allan Cameron said: "It happens two or three times a year to two or three animals."
He added: "We rarely catch the perpetrators because it normally happens when there aren't any staff around, early in the morning or late at night."
Cameron said it was common for dogs to chase sheep and they were easily confused and overtaken by instinct, leading to injuries. He said in most cases owners were horrified at the results
Cameron said rangers have a variety of tools to tackle the problem, from a friendly word to awareness-training days, dog-control orders and court action. Most people listen, he said, but not all.
The City of London Corporation, which manages 4,450ha of green space all across the capital, uses both cattle and sheep as part of its conservation-management work on much of its land.
Director of open spaces, Sue Ireland said: "We are seeing more attacks but the population is increasing and so is the number of people owning dogs. A lot of people don't realise that a dog will attack a range of wildlife given the opportunity.
"Part of the reason for bringing prosecutions is getting people to understand that if they are anywhere near any form of wildlife it is always safer to keep the dog on a lead."
Rangers face other dog-related problems. A small minority of dog owners use corporation land to train their dogs to be aggressive.
"We've had some evidence of other activity in our open spaces," said Cameron. "One of the things people who train dogs to fight do is tie them to a low-hanging branch on a tree. We've also had reports of people having dog fights. It is often associated with gangs." The authority always prosecutes illegal activity where possible.