The Housing Authority insists that tenants of Holmes Towers on the Upper East Side have embraced its ambitious plan to raise cash by building luxury apartments on what’s now their playground.

That’s news to them.

The tenant “stakeholder committee” organized by NYCHA to vet the plan — along with Manhattan Borough President Gale Brewer and City Councilman Ben Kallos — made clear in a recent letter obtained by the Daily News that they never signed off on it.