The UK Government has been asked to extend a temporary visa program, due to expire on February 28 next year, which allows drivers from overseas to help make up for shortfalls over the longer term.
"There is mounting concern amongst our membership that unless urgent action is taken, we will fall deeper into delivery chaos," WSTA chief executive Miles Beale said.
"We are already seeing major delays on wine and spirit delivery times which is pushing up costs and limiting the range of products available to UK consumers."
There are also calls for the government to help ease congested freight routes from ports.
The alcohol industry is one of the latest in an extensive list of sectors to warn of Christmas shortages due to supply chain issues.
Concerns have already been raised about the deliveries of items such as toys, trees and turkeys.