The government's drive to cut the number of overseas students coming to Britain will cost the country £2.4bn more than it saves, according to Home Office figures.

The official impact assessment for the reform of the student visa system shows the policy will cost more than £3.2bn over the next four years in reduced economic output and a further £330m in lost tuition fees and immigration visa fees.

Jonathan Portes, of the National Institute of Economic and Social Research, said: "The government has rightly said that economic growth is its top priority. It also has the commendable objective of rebalancing the UK economy away from consumption and towards exports. However, the Home Office's own impact assessment shows changes to student visa rules will reduce both growth and exports."

Home Office officials estimate that only £170m will be lost as a result of a reduction in tuition fee income to British colleges. But they admit the figure is "relatively uncertain", as it is based on the assumption that 80% of the lost places will be replaced by British and European Union students.

The official impact statement says: "[The] UK Border Agency [UKBA] believes that private further education and English language institutions are heavily reliant on non-EU students. On this basis we assume that businesses will strive to attract other nationalities of students (UK and EU), otherwise they would face going out of business.

"We believe a sensible replacement assumption would be 80%; so for every 10 non-EU migrants no longer able to study at all affected institutions we assume eight of their places would be filled by either EU or British nationals. In English language institutions, we assume that places will also be filled by either resident EU students or by students on the EU student visitor route."

The impact assessment also confirms that ministers expect 260,000 fewer student visas to be issued to non-EU nationals over the next five years as a result of the changes.

It also confirms that the drive to cut overseas student numbers will reduce overall net migration by around 48,000 a year between now and the next general election, when ministers have pledged to reduce annual net migration to the "tens of thousands".

The home secretary, Theresa May, officially notified parliament on Monday of the changes in immigration rules to implement the package from 21 July.

The impact assessment puts its "best estimate" for the cost of implementing the curb on overseas students over the next four years at £2.4bn, with a "worst-case" scenario of £3.6bn and an "optimistic" scenario of £1.3bn.

The "best estimate" is based on total costs to the economy of £3.5bn and benefits of £1.1bn, giving a net cost of £2.4bn.

The £3.5bn costs include £2bn for reduced output from students and their dependants who can no longer come to the UK, and reduced output from a change in student work entitlements. A further £1.2bn is accounted for by new restrictions on the ability of overseas students to stay in Britain to work after graduation. The loss in tuition fees is estimated at £170m and the loss in immigration visa fees at a further £160m.

Home Office officials admit they did not include any estimate for the potential impact on the growth of the British economy or any wider impact on the higher education sector.

The impact assessment does, however, outline benefits totalling £1.1bn, including £850m saved in reduced costs for public services, £75m from colleges reducing provision of courses and £150m saved by the UKBA in processing visas.

Matt Cavanagh, associate director at the thinktank the Institute for Public Policy Research (IPPR), said: "The government's own estimates admit how much money their clampdown on overseas students is going to take out of the economy, at a time when the recovery is fragile. The reductions have been scaled back slightly – a welcome sign that the government is listening.

"As with the cap on skilled workers, policy is still being driven by the political target on net migration. They should change it before it ends up causing real economic damage."

A Home Office spokesperson said: "We are required to provide impact assessments, but the process for these assessments is unsatisfactory. For example, they require us to assume there is a zero displacement effect of students taking jobs on the local labour market, and so we have asked the independent migration advisory committee to look at this issue."