Lidl in Chessington has approached nearby residents with above-market-value offers to buy their homes in an suspected expansion plan.
The Leatherhead Road store, built in 2008, has proved even more popular than the German company envisioned, with parking being a particular issue.
The Chessington district residents' association has said residents of Sussex Gardens, behind the shop, have been approached by the chain.
Chairman Jim Taylor said: "The people concerned have come and spoken to us.
"They are trying to buy properties in Sussex Gardens. They've been offering full market price, plus 10 per cent.
"That didn't seem to go down very well. They came back with the offer of buying half their gardens on the same principle.
"They seem eager to expand their parking area, but aren't being able to at the moment.
"All we know at the moment is that the Lidl's popularity has outstripped its space, and it's got to have more deliveries, for which it got permission.
"It doesn't have sufficient parking space to accommodate the customers that want to use it.
"This causes a bit of chaos out in the road. As they try to come in and leave they get all tangled up, especially when they go towards the south."
A Lidl spokeswoman said: "As part of Lidl UK's ongoing expansion plans we are always looking at different ways to improve our existing stores, which will often include researching opportunities to acquire additional land."
Lidl has previously faced complaints over the increased volume of its deliveries to Leatherhead Road, particularly from residents living above the store.
As a result of its unexpected success, the store was breaching its planning consent by having three stock deliveries a day instead of one.
Last year it successfully applied to increase the number of deliveries per day.
Lidl also owns the site of the former Organ and Dragon pub in Ewell, and last year unsuccessfully tried to buy homes surrounding the land.
A planning application for the site is yet to be submitted to Epsom and Ewell Council.
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