The UN has said more than 500,000 refugees had left Ukraine since the conflict began last Thursday.
Retired firefighter Ryk Matysiak from Barnsley said he has been inundated by donations since launching an appeal at the weekend.
He is planning to drive the goods to the town of Tomaszów Mazowiecki in central Poland later this month where his family, who are already helping refugees, can distribute them.
Mr Matysiak said: "We have promises of stuff from all over. We need clothes, toiletries, non perishable food, toys, bedding, mattresses, pushchairs - all the things people haven't got because they left in a hurry.
"We are also looking for advice with logistics, and help with transport, fuel costs and storage." He said getting storage space was crucial so he could get volunteers in sorting the goods out.
There are collection points at Subway, Parkway retail park, Sheffield (8am to 8pm); Mclintock business centre, Summer Lane, Barnsley (8am to 4pm) and Wortley private club (2pm till late). Mr Matysiak can be contacted via Facebook.