The Towers Cinema on Hornchurch High Street, which is 80 years old, will be bulldozed despite local residents opposing the plans.
Hundreds of residents signed a petition calling for councillors in Havering to protect the cinema and allow the Everyman cinema chain the chance to rescue it.
The cinema's facade will be taken down and the building - erected in 1935 - will be replaced by a glass-fronted discount supermarket.
A public meeting to talk over the plans for the cinema will take place on Thursday at North Street Hall from 5pm to 8pm.
Facebook campaign Save the Towers Building in Hornchurch posted: "Could have been an asset to our town but Lidl won.
"If this building is indeed to be demolished, as local people, should we be worried about lead-based paint and asbestos being disturbed?"
The Towers was a cinema until 1973 when it became a bingo hall as part of the Mecca bingo chain. Lidl reportedly bought the building for £8m last year, and the company says the store will create 40 jobs in the area.
A spokesperson for Lidl said: "Full consideration has been given to the application across this time period, including Historic England, who were consulted in November 2015 and confirmed that the secretary of state for culture, media and sport had decided not to list the building based upon the findings of a Historic England advice report, which assessed the building's historic interest and found that the criteria for listing were not fulfilled.
"We are aware and understanding of concerns raised by a number of local residents, and as a result plan to retain the 'Towers' lettering and create a public art installation at street level, integrating a piece of the site's past history within the new scheme and creating a focal interest on the frontage of the new store."