Church Action on Poverty was speaking after the government announced the current minimum wage of £6.50 an hour would increase by twenty pence to £6.70 an hour in October, marking a three-percent increase.
The increase on the statutory minimum wage for over-20s is the largest in real terms in seven years, and will affect more than 1.4 million low-paid workers.
However Church Action on Poverty is calling for employers to pay a living wage of £7.85 an hour outside of London, or £9.15 in London.
The charity also says many people who want full-time work are unable to get it, with many stuck on zero hours contracts which do not guarantee work.
It also commended churches in the UK for leading the way on fair pay by committing to paying staff a living wage, and criticised what it called the government's punishment of people in work by cutting certain benefits.
Liam Purcell, from Church Action on Poverty, told Premier: "It's obviously a welcome step. We've known for a long time the minimum wage is not enough to cover the basics that people need to get by.
"It hasn't kept with the rising cost of living, it's still not going to be enough to cover the basics.
"When it was first introduced we heard people saying it was going to cause unemployment and that really didn't happen. Businesses that pay the living wage find they have a much lower turnover of staff, much happier, healthier staff.
"It's very noticeable that while MPs have just agreed a pay rise of ten percent for themselves, we're still only seeing a rise of three percent for the hardworking people who are on minimum wage.
"All of the churches in the UK have now committed to pay the living wage to all of their staff and we're really pleased about that, they're setting an example to other employers.
"It's an aspiration we would like all employers to work towards. You should get a fair day's pay for a fair day's work."
Hourly pay rates for 16-17-year-olds are also increasing by two percent to £3.87 an hour, while the rate for 18-20-year-olds is rising by three percent to £5.30 an hour.
Apprentices are seeing the largest increase by percentages, with their minimum wage rising twenty percent to £3.30 an hour.
Listen to Liam Purcell speaking to Premier's Aaron James: