However, former pensions minister Sir Steve Webb said the additional 0.1 percentage point could cost the Government an extra £100m.
Sir Steve, of pensions consultancy LCP, said: “A slightly higher rate of increase is welcome for pensioners, though will be an unwelcome £100m extra cost for the Chancellor as she prepares her Budget.
“The rate of the new state pension will now be close to £12,000 per year, very near to the £12,570 tax-free personal allowance. This is likely to put extra pressure on the Chancellor to take action on tax allowances in the coming years.”
The 4.1pc figure will likely be the one used to uprate the state pension given that inflation was at 2.2pc last month. ONS inflation figures for September will be released on Wednesday.
The revised wage growth figure means the new state pension, for people who reached state pension age after April 2016, could increase from £221.20 per week to £230.30.
Meanwhile, the old basic state pension could increase from £169.50 a week to £176.45.
Around 350,000 retirees will be brought into income tax for the first time as a result of the state pension increase. This is because the tax-free personal allowance is frozen at £12,570, so many pensioners will be dragged into the tax net as their incomes rise above this threshold.