Bob Cratchit was NOT making less than the minimum wage.

Bob Cratchit was responsible for maintaining Scrooge’s account books, a job that involved much more than that of a simple bookkeeper today. His salary of 15 shillings a week made him poorly paid. Dickens chose that salary because he knew his readers would know this would be a low salary for such a position.
This salary, however, means he made more than the minimum wage. In today’s currency Cratchit’s annual wage would have a relative earnings value of £32,000 or $43,000. Today full-time work involves 2,000 hours per year (40 hours per week for 50 weeks). If we divide his computed annual relative earnings by 2,000 we find Cratchit’s hourly wage was £16 or $21.44.
The current minimum hourly wage in the United Kingdom is £ 8.91 or 55% of Cratchit’s hypothetical wage there. The current national minimum hourly wage in the United States is $7.25 or 34% of $21.44.
Thirty states, D.C., Guam and the USVI have a higher level. California at $13.00, Massachusetts at $13.50, Washington at $13.00, and the District of Columbia at $15.20 are the highest. None more that 70% of his calculated wage rate of $21.44.