Delivery trucks are permitted to unload at Aldi in Ludlow between 8am and 4pm on Sundays and bank holidays, but the global chain has applied to Shropshire Council to extend these hours to between 7am and 10pm.
The application is yet to be decided, but Councillor Andy Boddington said lorries have been photographed making deliveries as early as 7am in what he described as a "flagrant breach" of its planning permission.
Councillor Boddington, who represents Ludlow North, said: "Aldi is a multinational. This is not the first time it has broken planning rules.
"Clearly it doesn’t care about domestic matters such as the law of the United Kingdom.
"That’s a shame because the Ludlow Aldi is a good store with hard working and cheerful staff.
"They, and the residents of Ludlow, are being let down by a supermarket giant that clearly only cares about its own convenience and profit margins when it comes to delivery times."
Councillor Boddington said he had received complaints from several people who had seen lorries making early morning deliveries on Sundays.
"Aldi could have been honest and submitted a retrospective application. But that does not seem to be its style," he added.
"In 2010, it was forced to submit a retrospective application to deliver at 8am after a complaint that it was delivering well before 10am.
"Now it is breaking the rules again. I have had several people commenting that it is delivering earlier than allowed but today is the first time I have been able to get the evidence.
"It is quite clear that Aldi have decided to disregard any planning restrictions and do what suits it best.
"This retail giant seems to have no respect for the law or for Ludlow residents. That is a shame as it is a good store selling things that Ludlow residents need."
Ludlow Town Council has objected to the application to extend the opening hours, saying: "Delivery times should be curtailed to reflect those of neighbouring businesses."
A Shropshire Council spokesman said it did not currently have any planning enforcement cases in relation to the store.
An Aldi spokeswoman said: "Now we’re aware of this, we’ll remind our drivers of the permitted delivery times."