The following governmental organisations mandate Cyber Essentials:
Central Government Procurement
The government requires Cyber Essentials for all suppliers bidding for central government contracts advertised after 1 October 2014 which involve handling personal information and providing certain ICT products and services.
More information at GOV.UK - Procurement Policy Note 09/14
Ministry of Defence (MOD) Procurement
As of 1 January 2016, all suppliers bidding for new MOD requirements which include the transfer of ‘MOD identifiable information’ should achieve a Cyber Essentials Scheme (CES) certificate by the contract start date.
More information at GOV.UK - DCPP and cyber security controls.