Boris Johnson’s plan to increase national insurance contributions to raise £12bn for the NHS and social care could pose a “serious problem” for low-income workers, the archbishop of Canterbury has said.

Justin Welby said privileging wealthy pensioners over the poorest young people was “not a people-centred policy”, as he stressed the need for “intergenerational equity”.

His comments come after Tory MPs voted through a proposal to raise national insurance contributions (NICs) by 1.25 percentage points through a new ringfenced tax known as the “health and social care levy”.

Under the plan, patients entering the social care system from October 2023 will not have to pay more than £86,000 in their lifetime – excluding food and accommodation. More means-tested support will also be provided for those with assets of between £20,000 and £100,000.

The policy was announced earlier this week and put to a snap vote in the Commons in an attempt to stymie Tory rebels.

Concerns have been raised by the care sector, some Conservative backbenchers and thinktanks that ministers are failing to tackle the issue quickly enough by not implementing the social care changes for two years, and refusing to guarantee that people will not have to sell their home to pay even when the changes do come into effect. Some say the plan places an unfair burden on poorer workers.

Asked whether it was right that lower-income workers would pay disproportionately more, given pension and renting income was not covered by the levy, he said: “That is a very serious moral question. If we – as it were – privilege the wealthy older against the poorest younger, that will not work. That’s not a people-centred policy.

“The policy needs to be centred on people and care for the poorest, as well as ensuring that we have an embedded system that will work and is acceptable to all.

“As I say, the test is not just in terms of money, the test is in terms of effectiveness. If it pushes more young people into poverty and means they can’t get their own house and things like that, which I’m aware of from our own children – and ourselves for that matter, because we don’t own our house in this country – that is going to be a really serious problem, and that is wrong. It needs to be done fairly between the generations – that’s part of intergenerational reconciliation.”