Contractors have started work in the former bagel shop, hardware store and barbershop adjacent to the Big Y supermarket at 802 Williams St. in this suburb’s main shopping district. Work on converting that space into supermarket retail area will begin in earnest within weeks with completion expected within a few months, said Mathieu D’Amour, Big Y’s vice president of real estate and development. The Springfield-based supermarket chain is in the midst of getting final approval for the project from the town, he said. Town Manger Stephen J. Crane said Tuesday that Longmeadow officials will meet this week to discuss changes the town would like to see to the parking lot surrounding the Big Y. The town wants to see improvements to traffic flow and how deliveries to the store are handled.