Storey, who is chairman of Westbury Street Holdings - the parent company of brands including Benugo and Hix Restaurants - was recognised for his services to hospitality.
He also co-founded the front-of-house Gold Service Scholarship award, which counts the Queen herself as a patron.
Bangladeshi-born Miah received the award for his services to charity and the hospitality industry.
The chef opened the Raj restaurant in Edinburgh in 1991 and has since launched two Raj hotels in both London and the Scottish capital.
He also founded the Indian Chef of the Year competition to promote innovation in Indian cooking, and set up the Tommy Miah Institute of Hospitality Management training school in Bangladesh.
There was also an OBE for Beds & Bars chief executive Keith Knowles for his services to community and charity.
Restaurateur and designer Sir Terence Conran, co-owner of Bibendum, became a member of the Order of the Companions of Honour for his services to design.
He founded Conran restaurants in 1991 before the company (now D&D London) was sold to Des Gunewardena and David Loewi in 2007.
Conran was involved in the creation of restaurants including Bluebird Chelsea, Le Pont de la Tour and Bibendum, which he re-launched with Claude Bosi this year.