Melburnians have been warned not to swim at any of Melbourne's three dozen monitored beaches today because of pollution expected to run into the bay following heavy rain.

The Environment Protection Authority yesterday advised people not to swim near stormwater drains, rivers, streams and other outlets into the bay during and for at least 48 hours after rainfall.

The Age revealed last year the Mobil refinery at Yarraville would be able to continue pumping millions of litres of industrial waste water into the Yarra River under an amended licence issued by the EPA.

Dozens of other EPA licences allow the discharge of treated sewage and industrial cooling water into creeks and rivers across Victoria.