The couple are concerned the takeover will put jobs at risk. Their three cafes employ about 50 members of staff during the summer and 30 over the winter.
Lido regular Kate Orr, 56, from Camden, said the cafe was part of the community.
Imogen West, 56, from Hampstead Heath, added: “This area is a real mix of people who do have money and people who don’t. This place serves all of those people.”
The Italian cafe at Parliament Hill Fields has been run by the D’Auria family for 45 years.
Journalist Stefan Simanowitz, 49, said he was outraged by the CLC’s decision and would continue to fight it.
He ran a “save our cafes” campaign, which included a petition signed by more than 20,000 people and was supported by Cumberbatch, McAvoy and fellow actor Stephen Campbell Moore.
In 2016, a similar re-tendering process was attempted at Parliament Hill Cafe, but coffee chain Benugo dropped out of the takeover following protests backed by Sir Keir Starmer, MP for Holborn and St Pancras, who is now prime minister.