There is no need to impose equality laws on private firms because each private company can have its own rules on equality. If they break their own rules, employees will be free to take them to an industrial tribunal, since these rules will form part of their contract of employment. If a company does not take equality seriously, consumers and workers will be free to boycott that company. There is no role for the state in all of this.
For the state to impose its own ideas of equality on everyone is an infringement of basic freedoms and flies in the face of the fundamental principles of a liberal democracy.