Mooky Greidinger says when they reopened from lockdown, the situation was 'good'.
But pressure's since been mounting due a delay in several blockbuster films being released.
It puts up to 5,500 jobs here at risk.
The British chain's sites in the US will also shut.
The Feltham Cineworld has been described as a "leader in its field", showing the most Bollywood films outside of Mumbai.
Feltham and Heston MP Seema Malhotra says she's writing to the government.