Rising unemployment will cost the government £1.5bn more than expected in welfare benefits, according to official forecasts that reveal the hidden cost of the coalition's austerity drive.

As big increases in VAT are due to bite from Tuesday, analysis from the Office for Budget Responsibility shows slowing economic growth will make it harder to reduce the deficit by forcing more people to seek state support.

The Treasury watchdog calculates the government will have to pay out £700m more in unemployment benefit than previously forecast. Similarly, a higher number claiming jobseeker's allowance as well as falling into lower wage brackets will see the government needing to pay out another £700m more in housing assistance over the next four years.

Though the OBR data, released last month, confirms the government is still making substantial savings from its changes to both benefits, the shadow work and pensions secretary, Douglas Alexander, said the OBR's fresh assessment suggested it was government strategy that was leaving these higher numbers exposed.

He said: "The growing cost of the risk the government is running with the economic recovery is now emerging. The result of policies which undermine growth and jobs is a longer dole queue and a higher welfare bill."

The new higher official cost of supporting those claiming unemployment benefit comes as some economists warn of unemployment rising from 7.5 to 8.4% at the end of the year. Many are braced for the first squeeze on the economy when VAT is increased at midnight tomorrow night.

Today the Labour leader, Ed Miliband, will hit the campaign trail in the Oldham East and Saddleworth byelection seeking to make the VAT rise a central issue, saying it is the "wrong tax, wrong time". Labour will put up posters the Liberal Democrats themselves ran on before the general election warning of the "Tory VAT bombshell" and said a Conservative government would make the average British family pay £389 extra in VAT a year was a reason to vote Lib Dem.

In a speech tomorrow, Miliband will say that families will pay £7.50 a week because of the Lib Dems' "broken promise". This week Lib Dem heavy-hitters will hit the campaign trail as well with the party leader, Nick Clegg, in the seat on Wednesday; the party president, Tim Farron, tomorrow; three ministers on Tuesday; the former leader Charles Kennedy on Thursday and deputy leader Simon Hughes on Friday. The election is on 13 January.

In his speech Miliband will say: "Today we start to see the Tory-led agenda move from Downing Street to your street. At midnight VAT goes up, hitting people's living standards, small businesses and jobs. The VAT rise is the most visible example of what we mean when we say the government is going too far and too fast."

Overall, economists believe 2011 will be another tough year, with growth expected to slow sharply in the first half of the year. This is likely to lead to another round of job losses as the government slashes spending and private sector firms also cut back, and some see the unemployment rate hitting 8.4% by the end of 2011, from the current 7.9%.

City economists are predicting 1.9% economic growth for this year, which is less optimistic than the Office for Budget Responsibility's 2.1% forecast. The Paris-based Organisation for Economic Co-operation and Development believes the UK economy will grow by just 1.7%.

Howard Archer, at IHS Global Insight, said: "Some temporary growth drivers will wane, while the economy faces the fiscal squeeze increasingly kicking, starting with the VAT hike in January, as well as an uncertain global growth outlook.

"In particular, the current heightened turmoil in the eurozone could negatively impact on the UK economy, particularly through hitting exports."

The document released by the OBR is the unit's revised costing of figures contained in June's budget. Before that in the OBR's pre-budget forecast they predicted the unemployment claimant count for 2011-2014 to be 1.4m, 1.3m, 1.2m and 1.1m respectively but in the budget two weeks later they were each revised to be 100,000 higher and the OBR has only now upgraded the cost of these new values.

The new higher levels of cost are based on the OBR's own predictions of unemployment. While before the June budget the OBR said unemployment would be 6.3% in 2014, after the budget they said it would be 6.5%. The costing it released in December is based on this document. They have since released another prediction – in November, though they reported better than expected unemployment for next year they nonetheless predicted that 2014's level would be 6.7%. The OBR has not yet produced costings for this last new level with the potential that government expenditure could go up.

In an article for the Guardian today, Alexander says the Labour party has still got much work to do to prove it is credible on the economy.

He writes that Labour needs to understand "why people turned away from us, including concerns about the deficit, and pursuing a tough and sustained course to show that we can be trusted with the nation's finances... [There] shouldn't be an excuse for any of us in the Labour party, to deny the need for difficult decisions on public expenditure and instead focus solely on attacks on the government."