Can a salary-sacrifice arrangement reduce an employee's pay to below the national minimum wage rate?

No, a salary-sacrifice arrangement must not reduce an employee's wages to below the level of the national minimum wage.

A salary sacrifice occurs when an employee gives up part of the wages due under their contract of employment, usually in return for some form of non-cash benefit, such as childcare vouchers, an employer-provided nursery place or permanent health insurance. The sacrifice is achieved by varying the employee's terms and conditions of employment relating to pay. Apart from living accommodation (for which there is a daily offset), non-cash benefits in kind that are provided instead of wages do not count towards the minimum wage (reg.10 of the National Minimum Wage Regulations 2015 (SI 2015/621)). It makes no difference whether or not the benefit is taxable. 

Employers must monitor the impact of salary sacrifices on employees' wages to ensure that they do not fall below the relevant national minimum wage rate.