The met office also predicted widespread rainfall in the southern districts over the next three days.
Two persons died and eight others were injured in North 24 Parganas district, while two persons were killed in South 24 Parganas district, when they were struck by lightning, an official said.
A boy was killed in Purulia district due to lightning strike, the official said, adding that a youth drowned in Sutunga river in Mekhliganj in Cooch Behar district during the rain.
The downpour affected services of Eastern Railway and South Eastern Railway, as speed of trains had to be curtailed following waterlogging on tracks.
In Kolkata, important areas like the Eastern Metropolitan Bypass, Mahatma Gandhi Road, Syed Amir Ali Avenue, Behala, Khidirpur, Ultadanga and Patipukur underpass saw accumulation of water as the skies opened up from the early hours.
Traffic moved at snail's pace, office-goers and school children were inconvenienced, and taxis fleeced commuters - all familiar scenes in rain-hit Kolkata.
"In the EM Bypass area there was a drainage system which has got choked due to which the area has become waterlogged. I have visited the area along with other officers. We are working on a Detailed Project Report for coming up with a new drainage system and we will arrive at a solution soon," said KMC Mayor-in-Council, drainage, Tarak Singh.
A Met department bulletin warned of "heavy to very heavy rainfall (7-20 cm)" in most places of Darjeeling, Kalimpong, Jalpaiguri, Cooch Behar and Alipurduar districts from June 25 June 29, "caused by an upper air cyclonic circulation over West Assam and sub-Himalayan West Bengal".
It said several south Bengal districts would also be affected by incessant rainfall over the next three days and issued an alert for North 24 Parganas and South 24 Parganas and East Midnapore districts.
"Rainfall in most places likely over south Bengal districts due to a cyclonic circulation that lies over northwest Bay of Bengal," the bulletin added.
The maximum rainfall received till 10:30 a.m. Monday is 33.4 mm with relative humidity at 92 per cent.