The north Lincolnshire-based firm won a contract to supply around 80,000 trees and shrubs to the council that it must fulfil by the end of January.
The contract is part of the local authority's annual grant scheme, which encourages tree and hedgerow planting as well as providing replacements for landowners who have removed dangerous trees.
The seven staff at British Hardwood must now collate around 300 separate orders for delivery to the council, schools, communities and farmers.
Managing director Andrew Henderson told HW that it was an encouraging to start the year with a substantial contract. "We are working flat out," he said. "It has been a challenge with the frost and snow, but we are working around it."
As well as providing mixed broadleaf species including oak, lime, ash and hawthorn, the firm will also supply associated planting products such as tubes.
Henderson added that online sister firm gardensupplies.co.uk had helped the company to ensure year-round business.
Although the online gift and garden products shop only launched in March 2009, it had already been a success, he said.
"We had a real peak towards Christmas," explained Henderson. Running an online promotion offering free trees to those spending more than £40 had also helped, he added.
"Grow-your-own products have also been successful and I think that trend will continue in 2010," he predicted.