The report, which was published on 26 July and produced in association with data company Spend Network, looked at 38m transactions from 247 central and local government organisations. It found that the only other sector which saw a spending increase was utilities, which rose by 28% to £282m in 2013.
The top 20 suppliers to central and local government accounted for at least £10.2bn of government expenditure in 2013. Six of the top 20 suppliers to government are IT suppliers, six are construction companies and two are business process outsourcing companies.
According to the data, IT company HP is the largest single supplier to government, followed by Capgemini, another IT company.
The report also found that four of the top 20 suppliers appear to be heavily reliant on one department for their central government revenue.
While the IfG praised the government's commitment to publish spending data, it also warned that information was difficult to obtain and analyse and might therefore include inaccuracies.
IfG researcher Gavin Freeguard said: "It reflects well on the Government's commitment to transparency that we've been able to produce this analysis of independent suppliers to government.
"Nonetheless, this research shows how difficult it is to analyse who is contracted to provide our public services and what it costs."
The report calls on the government to improve its open data in order to be able to understand spending on individual contracts, particularly relating to small and medium enterprises (SMEs) and through Private Finance Initiative (PFI) deals.
It recommends improvements in the way central government reports spending, and argues there is not enough data - particularly further down the supply chains - to verify government claims that Whitehall is on track to place 25% of government spend with SMEs.
It said: "The data is published in a way that makes it hard to determine which companies ultimately benefit from payments relating to PFI contracts and joint ventures; is limited in accuracy due to the fact that some datasets are not published; and is constrained by the fact that central government transactions under £25,000 are rarely published."
Jeni Tennison, technical director of the Open Data Institute said: "Providing more consistent and higher quality open spending data would enable more robust conclusions, and there is still not enough open data available about contracts and the performance of suppliers."
The IfG recommends that the government lower the £25,000 threshold for publication of public sector transactions to £500 for all public sector bodies.
A Cabinet Office spokesperson said: "Through our long-term economic plan we have done more than any other government to open up contracts and address long-standing weaknesses in commercial skills. Before 2010 no one knew who government suppliers were, nor how much business SMEs won.
"We are levelling the playing field for smaller companies and growing a more diverse market for suppliers, but there's more to do - particularly as major legacy contracts expire in the years ahead.
"We welcome this analysis which draws on our published data and will look at how we can go further with our transparency."