12:55PM, Monday 24 June 2013
The swans had to be rescued by volunteers at Eton charity Swan Lifeline on Friday night and were cleaned across the weekend.
An EA spokeswoman said: "We are still investigating the source of the oil and therefore we cannot confirm where it originated.
"However, owing to the nature of the incident and the fact that the oil dispersed fairly quickly it is likely to have been illegally disposed down a surface water drain."
The charity hopes to release the swans back into the river sometime tomorrow around noon.
Oil can cause a swan to sink as it affects its water-proofing and each had to be cleaned in communal tubs with washing up liquid.
There are about 200 swans on the river in the Windsor area.
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