The store, in The Broadway, is one of 34 branches across the country to cease trading.
The shops closing were bought from the Co-op by The Food Retailer Operations Limited (TFR) and traded under the Budgens brand.
But since its acquisition of the stores TFR has experienced difficult trading conditions which resulted in the company being placed into administration.
Following the appointment, joint administrators Michael Denny, Robert Moran and Matthew Hammond of PricewaterhouseCooper (PwC) have been assessing interest in the business.
Many of the stores around the country were closed on February 26 and Sunday (March 5).
The Southall store is among the final group of branches which will cease trading.
The closures will result in the loss of more than 800 jobs in total across the country.
Joint PwC administrator Mr Denny, said: “Unfortunately, we have been unable to find a buyer and it is not commercially viable to continue trading the stores.
“We are working closely with the Co-op, USDAW and the relevant government agencies to ensure that all employees receive the maximum levels of practical and financial support through the redundancy process.”
Budgens distanced itself from the closures, with a spokesman saying: “Budgens is a brand which operates 150 stores as a symbol group.
"The business is performing very strongly.”
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