Sir Kevin Collins resigned on Wednesday, claiming the package “falls far short of what is needed”.
Geoff Barton, general secretary of the Association of School and College Leaders union, described it as a “desperately bleak week for education”.
“It is abundantly clear that a recovery programme is urgently required at a scale and scope to address this massive issue,” he said.
“We once again call upon the prime minister and the treasury to step up and urgently provide the substantial recovery programme that children and young people need and deserve.”
Jon Andrews, co-author of the study, added: “We need to continue to look at how we can support all pupils through effective catch-up programmes, but especially those from disadvantaged backgrounds, whose education has seen the most damage from the pandemic.”