The fastest, cheapest and most convenient way would be to take a cab, bus or ac bus from Howrah to Esplanade/Dharamtala and take a Metro from Esplanade straight to Kalighat.
There may be rush in the Metro during office hours.
A direct AC bus from Howrah to Kalighat is also frequently available which would be very nice and comfortable too.
Bus No. AC1, AC5, AC6 AND AC24 are AC buses directly from Howrah to Kalighat.
From inside Howrah station platform#1 take the left subway pedestrian that will take you directly to the bus stand.Edited: 17 January 2018, 05:51
Thanks for the information, which is most useful. However i would like to mention that I will be arriving at Howrah at 4-50 Am on a Saturday and a search on the net shows that AC buses and Metro start much later. I would have to wait a long time to catch these, if the information is correct. Is there any suitable alternative?
If that is the case then please opt for Uber/Ola or Pre Paid Cab.
Pre Paid counters ar just outside the Stations and the rates would be reasonable.
Don't fall in prey of post paid taxis or post paid taxis offering you a pre paid rate. Buy your slip from the Pre Paid counter and it would have the Cab No. and Lane printed from where you can board immediately.
Thank you for the information.