The living wage of £7.20 per hour was introduced in April, benefitting more than a million staff aged 25 and over.
Some business organisations have been lobbying the government to restrain future increases in the hourly rate.
But the Resolution Foundation said that women, the young and older workers were most likely to lose out if future rises are limited, reports the BBC.
Conor D’Arcy, policy analyst at the foundation, said some businesses were unhappy about a higher minimum wage, but the wage policy was pegged to typical hourly pay and therefore reflects changing economic circumstances.
Abandoning increases “would also be costly for millions of low paid workers, so the prime minister should stick to her guns”, he said.
After the Brexit vote in June the government was lobbied by 16 trade associations who called on ministers to be cautious about future increases in the national living wage.
Low-paid workers are due to get above-average pay rises over the next four years as the policy approaches its target of paying 60 per cent of average hourly pay.
Based on independent economic forecasts published by the Treasury, the Resolution Foundation expects it to rise to about £8.70 in 2020.
That is lower than the £9 forecast in the March 2016 Budget because overall wage growth is expected to weaken.
The projected figure for 2020 is likely to fluctuate in coming years as wage forecasts are updated and the impact of implementing Brexit becomes clear, the foundation added.
Ripple effect
The think-tank has previously estimated that by 2020 the national living wage should benefit more than six million workers.
Many are predicted to gain directly, while some will benefit from a “ripple effect” as the new policy pushes up wages more generally.
The Low Pay Commission will meet in October to decide its recommendation for next year’s national living wage increase.
The Resolution Foundation says that if there were no further increases relative to average hourly pay, then by 2020 low paid workers would lose as much as £1,500 from their prospective annual pay.
In early August, 21 trade associations wrote to the new business secretary, Greg Clark, asking him to “exercise caution” on the rate at which the living wage might rise, because of “economic uncertainties the country faces” after the Brexit vote.
A spokeswoman for Theresa May appeared to brush that aside, saying: “The prime minister has been clear about building an economy that works for everyone, and making sure that people earn a decent wage for a day’s work is an important part of that.”
