Unions welcomed the £7.20 hourly rate for adults - increasing by 50p from £6.70 - but said it was not fair that younger workers were missing out, while business groups warned that firms' pay bills will "ratchet up".
The Government's aim is to increase the rate to £9 an hour by 2020, which would affect an estimated nine million workers.
But the rate is well below the Living Wage set by the Living Wage Foundation which is currently £8.25 and £9.40 in London.
Revd Steve Chalke runs a number of schools and churches with his Oasis Foundation.
On Premier's News Hour he said: "We are a living wage payer. In London that means that we already pay £9.40 an hour which is significantly higher than the £7.20 that the government have introduced today. So even those it works for, it doesn't work that well for.
"It says to a person that they're valued, it gives them a stake in society, it's a step along the way. We've got a lot further to go. We've got to enfranchise the under-25s as well as the over 25s. This is a good start but there's a long way to go.
"To all those who don't pay the living wage, it really makes sense for a just society.
"Paying well is good for business, it's not bad for business. I've found that as we honour and value our staff, they enjoy being here and stick around.
"Research shows that if you pay the living wage, the quality of work that you get from your staff increases because their commitment to you increases. You'll recruit better people and you'll retain better people."
Katherine Chapman, director of the Living Wage Foundation said: "Today's new legal minimum is an important step forward in tackling low pay in the UK. The landscape on low pay has shifted. This is down to the employers we work with who have over the past 10 years voluntarily chosen to pay beyond the minimum wage rates set by Government.
"However the job is not done when it comes to tackling low pay. Around six million people earn below the voluntary living wage with women, young people and part time workers most affected by low pay."
The Government said the new rate will mean a £900 cash increase for a full-time worker on the current national minimum wage.
Chancellor George Osborne said: "The national living wage will play a central role in moving Britain to a higher wage, lower tax, lower welfare economy.
"It will also mark the end of the gender pay gap for some of our lowest paid and hardest working people."