A senior Tory minister has claimed the introduction of the new living wage will “fuel” immigration if Britain votes to remain in the EU.

The Culture Secretary, John Whittingdale, who has already pledged allegiance to the campaign to leave the EU, said those coming from outside the UK could benefit most from the policy.

His comments are likely to frustrate some in the Conservative camp - in particular George Osborne, who sees the wage increase as one of his flagship policies - as the party’s divide over Europe intensifies.

“The living wage was a great idea to give British families a pay rise, but because we have no control of our borders the main people that benefit could be from other EU countries,” Mr Whittingdale told The Times.

“Wages in the UK will be so much higher than the rest of Europe that this will fuel even higher levels of immigration, putting great strain on our schools and hospitals.

“If we vote Leave and take back control, we will be able to ensure that workers who are currently in the UK will get the full benefit of the rise in the living wage,” he said.

However, Labour MP Chuka Umunna said those objecting to the policy were wrong because the living wage had little to do with the EU referendum.

The National Living Wage is a statutory minimum wage.

The higher rate will see UK workers over the age of 25 get a pay rise of 50p, increasing the current hourly rate of £6.70 to £7.20. The rate is set to rise to £9 by 2020.