"The supermarket has still not made its way to official accreditation, which is the only public guarantee that its workers' pay will continue to keep pace with the future cost of living", she said.
More than 150,000 workers will get an inflation-beating pay rise on Monday as the United Kingdom living wage, which is paid voluntarily by more than 3,600 employers, is increased against a backdrop of rising transport, food and housing costs.
Inside the M25, wages are set to rise by 4.6 per cent from £9.75 to £10.20 per hour.
"The new rates will bring relief for thousands of United Kingdom workers being squeezed by stagnant wages and rising inflation", Living Wage Foundation Director Katherine Chapman said.
"It's thanks to the leadership of employers across Scotland who are committed to paying all their staff, including cleaners and security staff, a real living wage".
The retailer said the move would directly benefit 16,000 staff and make them the highest paid supermarket employees in the UK.
It differs from the government's national living wage, which replaced the minimum wage for workers aged 25 and over in April 2016.
For those living in London, the rate will increase by 45p to £10.20 an hour.
KPMG UK director Andy Bagnall said more work had to be done to end in-work poverty.
"We firmly believe that paying the living wage is the right thing to do as a responsible employer", Heathrow Chief Executive John Holland-Kaye said.
The Living Wage Moment are bringing on board Auckland electricity and gas distributor Vector Limited as an accredited Living Wage employer.
"It is clear that it may not be possible or practical for everyone, but businesses need to do what they can to address the problem of low pay. We encourage other employers in Oxford to adopt the Oxford Living Wage". Profits in the United Kingdom are at record levels, yet many bosses are still refusing to invest in their staff. However, more than 1,000 employers have signed up to the measure since a year ago, "putting fairness and respect at the heart of their business", Chapman added. You can check which companies are signed up on the Living Wage Foundation website.