Images shared on the councillor’s Twitter page appear to show several shopping trollies, a children’s play house, traffic cones and litter strewn across the burn.
The local councillor said in a post that he believed there to be as many as a dozen shopping trollies in the water and on the embankments.
The Braid Burn runs through the popular Colinton Mains Park and the debris is said to be causing severe damage to the local eco system.
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Councillor Arthur said: “Oxgangs and Firrhill in my Ward are great areas, but they are held back by the tiny minority of people that think tipping is acceptable.
“Colinton Mains Park is a great resource, and the Braid Burn should be its highlight. Instead, selfish people have turned it into an embarrassment. They should be ashamed.”
Councillor Lesley Macinnes, Transport and Environment Convener said: “It’s very disappointing to see so many trollies dumped in the burn. Fly-tipping is selfish, dangerous and harmful to the local environment and those responsible should reconsider their anti-social actions. We will work to get the burn cleared of these as soon as possible, which is, of course, an additional, unnecessary cost.”
A spokesperson for the Scottish Environment Protection Agency (SEPA) said: "Fly tipping is not only unsightly but, depending on the nature of the waste, it can also be hazardous to health and cause environmental damage.
"SEPA would urge members of the public to utilise waste recycling centres to safely dispose of any unwanted waste. Anyone you use to take your waste away should be able to provide a waste carrier registration number and tell you the named facility they will take the waste to – if they can’t provide this information, don’t allow them to take your waste. You can check the waste carriers licence for any company or individual you are thinking of using at sepa.org.uk/wastecarriers.
"We would encourage anyone that witnesses any fly tipping incidents to report it immediately through the Dumb Dumpers website at www.dumbdumpers.org.uk or if the incident is ongoing or believed to be of a hazardous nature report the incident using our 24-hour online form at www.sepa.org.uk/report."