Security guards and catering staff at the Sellafield nuclear reprocessing plant in Cumbria have begun the first of two 10-day strikes over pay.
About 180 workers employed by outsourcing firm Mitie want an increase in their current hourly rate of £8.45.
The firm said it only negotiated with the GMB union at Sellafield, but that all staff had benefited from pay rises.
Sellafield Limited said it was monitoring the situation, but had contingency arrangements in place.
The union had originally planned to strike from 19 April but postponed the stoppage in the hope of fresh talks.
However, the union said no fresh offer had been made.
A further strike is due to start on 4 May.
According to the government website, the National Living Wage and the National Minimum Wage rate from April 2019 is £8.21 for those aged 25 years and above, prior to that it was £7.83.