Flood warnings have been issued across Melbourne and much of western Victoria as a damaging front moves in, bringing heavy rain and wild winds.

The Yarra, Werribee and Maribyrnong rivers, which all run through Melbourne, are included in widespread flood warnings issued by the Bureau of Meteorology on Wednesday afternoon.

“A cold front will move eastwards across Victoria today, bringing areas of heavy rainfall and thunderstorms to the northern part of the state,” the BOM said.

It said there had already been widespread rainfall of up to 25 millimetres across much of the state, with falls of more than 120 millimetres possible in coming hours as the front moved east.

Many catchments in central and north-eastern Victoria were already wet, increasing the risk of flooding, the bureau said.

“Widespread rainfall totals of 40-60 millimetres are expected in the flood watch area from Wednesday afternoon into Thursday, with isolated heavier falls of 60-80 millimetres possible with thunderstorms and about higher terrain,” it said.

“Isolated totals in excess of 120 millimetres are possible over the higher peaks in the north-east.”

The warning said rivers within the flood watch areas – which cover much of the state – are likely to rise. Flooding is likely in affected areas from late on Wednesday.

Those areas include much of northern and north-west Victoria that was hit by devastating flooding last October. There was also flooding in Melbourne’s inner-north-west from the Maribyrnong River.

Prime Minister Anthony Albanese reportedly cancelled a planned visit to Horsham, in western Victoria, due to the weather warnings. There was also a flash flood warning for Halls Gap, in the tourist spot of the Grampians on Wednesday.

The warnings for Victoria come after a lightning storm brought heavy rain across South Australia, leaving thousands without power and causing widespread but minor damage early on Wednesday.

The worst of the weather hit Adelaide about 3am, with falls of close to 30 millimetres drenching some suburbs in about an hour.

There were also about 83,000 lightning strikes across South Australia.

SA Power Networks said about 8500 customers remained without electricity with outages spread from the Eyre Peninsula, through the mid-north, across Adelaide and the Adelaide Hills and down to the southeast.

The State Emergency Service said it had responded to about 30 calls for assistance with incidents ranging from trees down to minor flooding.

It said more calls were likely as people discovered further damage during the day.

The BOM said rain would become less likely over Adelaide during Wednesday. The city was forecast to receive another 10 millimetres of rain on Thursday.

-with AAP