In its regular assessment of UK plc's prospects, the CBI raised its growth forecast for this year from 2.6% to 3%.
But it also highlighted concerns that the recovery could be derailed by uncertainty around the general election, urging politicians to push ahead with boosting the supply of homes and taking decisions on major infrastructure projects.
Director-general John Cridland said property values were expected to rise by 8.2% this year and 5.1% next.
He said:
"We have to remain alert to the risks posed by unsustainable house price inflation, and the Bank of England Financial Policy Committee is poised to act when necessary. Housing has come back under the spotlight as annual house price inflation figures have reached double digits on some measures. While housing transactions are still running almost 30 per cent below their last peak in 2006, they are picking up steadily."
Although London house prices have risen 25 per cent above the 2008 peak, this has in part been fuelled by foreign cash buyers.
He added: "Outside London, prices remain around 2 per cent below peak figures with an even greater difference when you move outside the South East."
The CBI previously predicted that the Bank would have to start raising rates in the third quarter of next year - but has now brought that forward to the first quarter.
Mr Cridland declined to say whether the UK Government's Help to Buy scheme - which offers guarantees so that people without large deposits can get mortgages - should be wound down. But he suggested the initiative was only having a marginal impact on the market, with the overwhelming majority of purchases in which it is used taking place outside London.
He added that it was crucial for governments to focus on increasing housing supply.
The CBI's assessment said political uncertainty remained a "major risk to the recovery" and parties needed to show they would "stick with what is working" after the election.
Chief policy director Katja Hall said:
"That means the new government, of whatever colour, keeping the deficit reduction strategy on track. It must also tackle the UK's economic challenges and not duck the tough decisions, such as reforming public services. Political positioning must not be allowed to stifle investment, whether it's an unrealistic immigration target, unjustified interventions into specific markets, flirting with leaving the European Union, delaying vital long-term infrastructure projects or restricting labour market flexibility.
Pre-election pledges should not deter overseas and home-grown investors and entrepreneurs, nor limit a future government's ability to deliver prosperity in the UK."
Ms Hall said the next government needed to commit to implementing the conclusions of the Davies Commission on how to increase aviation capacity.
Housing Minister Kris Hopkins said:
"The Government is committed to delivering long-term economic stability and economic growth. The last administration oversaw a housing boom and bust and we've been picking up the pieces.
"Mortgage lending activity in the housing market and loan-to-value ratios on new mortgage lending remain below their historic averages. And while the price rises we're seeing at the moment are nowhere near what they were at the height of the unsustainable housing boom, they are a sign of how the economy is recovering from the downturn.
"For those wanting to get on the housing ladder, we have introduced schemes like Help to Buy. This means that people can get on the housing ladder with a fraction of the deposit they would normally require. And it's why we've tackled the deficit, to help keep interest rates low and mortgages more affordable."
