Home secretary Priti Patel has overridden objections from civil servants to press ahead with contentious plans to send migrants who seek asylum in Britain on a one-way ticket to Rwanda.

Patel took the rare step of issuing a so-called ministerial direction to enable her to overrule officials’ concerns that the plans would not offer value for money.

Boris Johnson has been strongly criticised by opposition politicians and human rights groups after he said on Thursday that anyone who has entered Britain through irregular means since January 1 and not sought asylum in a safe third country may be transported to Rwanda and assessed in the African country for eventual resettlement.

The prime minister announced a new government scheme that could involve sending tens of thousands of migrants to Rwanda, as part of a strategy to tackle gangs that use boats on the English Channel to bring people from France to the UK.

A ministerial direction was issued by Patel this week to overrule civil servants’ concerns about the scheme, which partly focused on the difficulty of quantifying its financial impact, according to officials briefed on the matter.

One Home Office insider said: “Home Office officials are clear that deterring illegal entry would create significant savings. However, such a deterrent effect cannot be quantified with certainty.

“It would be wrong to let a lack of precise modelling delay a policy aimed at reducing illegal migration, saving lives, and breaking the business model of the smuggling gangs.”

Patel’s allies said the current asylum system costs taxpayers £1.5bn a year and £5mn is being spent on hotels each day for those who have arrived illegally in the UK.

Ministers are braced for significant legal challenges to the plans.

Tom Pursglove, minister for tackling illegal migration, acknowledged the plans would be “difficult” for the government to implement but argued there was a “moral imperative” to try to break the business model of people smuggling.

“What is cruel and inhumane is allowing evil criminal gangs to take advantage of people, to take their money, to put them in small boats, often with force, including women and children, to put them in the Channel with all the risks that that presents to human life,” he told ITV.

The cost of the scheme has been criticised: the UK has agreed to pay £120mn to Rwanda and is likely to incur other expenses.

Pursglove said the scheme would save money in the “longer term” and it would comply with the UK’s legal obligations.

But Andrew Mitchell, the Conservative former international development secretary, said the costs would be “eye-watering” and doubted whether the plans would be successful in deterring people smugglers.

“The government is quite rightly trying to break the smugglers’ sordid and deathly model and so I am absolutely behind them in doing that. The problem with the scheme that they have announced is that I don’t think it will work,” he told the BBC.

Gillian Triggs, assistant secretary-general at the UNHCR, UN refugee agency, said that the body “strongly condemns outsourcing the primary responsibility to consider the refugee status”.

She told the BBC that the policy was a “troubling development”, particularly in light of the millions refugees fleeing Ukraine.

When asked to compare Johnson’s policy to similar tactics used by Australia, she said: “Just as the Australian policy is an egregious breach of international law and refugee law and human rights law, so too is this proposal by the United Kingdom government.”

Downing Street hopes the first migrants will be sent to Rwanda “in weeks, or a small number of months”, according to Andrew Griffith, Number 10’s director of policy.