Ms Gibb claimed the NHS had "unjustly enriched itself" at her expense by failing to pay the compensation and sought to enforce the rest of her severance agreement at the High Court.
It alleged present-day companies and their predecessors, were "unjustly enriched through profits earned either directly or indirectly from the Trans-Atlantic slave trade and slavery between 1619 and 1865, as well as post-Emancipation slavery through the 1960s".