After years shaking off the hangover of a debt-fuelled property boom, these are rare times for British housebuilders. Rescue rights issues and restructurings were the norm in the wake of the credit crunch as the mortgage market dwindled overnight. But now we have that rarest of things: a housebuilder emerging from the sick bay and preparing to dip its toe back into public markets.

Crest Nicholson's £500m float is the first significant initial public offering in the industry for a decade, and is likely to be followed soon after by the retirement builder McCarthy & Stone. A look at the FTSE 350 general housebuilders' index – up 32 per cent in the last year alone – explains why. Building on cheaper land bought since the crash is fattening profit margins without any significant rise in volume growth, share prices and dividends are rising, and lenders who supported the strugglers through the downturn are sniffing an exit.

Another prime mover is the Bank of England's Funding for Lending scheme, launched last August to allow banks to access ultra-cheap funding lines in return for growing net lending. The cash, albeit drawn down in small amounts so far, is finding its way far more quickly to the mortgage market than corporate credit. Lending rates are coming down, and the Bank's own credit conditions survey says banks and building societies are gearing up for a "significant" increase in credit availability during the current quarter.

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The Government is also doing its bit to help the market with its NewBuy and FirstBuy schemes, to help first-time buyers bridge the deposit gap to get on the ladder as well as increase the availability of 95 per cent loan-to-value mortgage loans. But this influx of funds into the mortgage market is not being matched by an increase in supply of homes, according to the bosses of the country's two biggest housebuilders. Economics dictates that if supply fails to keep up with rising demand, the result will be rising house prices. So is the Bank of England at risk of fuelling another house price boom?

The figures are stark: in 2007 builders completed 170,000 homes, and in 2011, the last full year available, this fell to 109,000. This is barely 6,000 above the nadir touched in 2008, which saw the lowest year for completions since 1923. According to official estimates, we need 232,000 homes a year to be built to keep up with the formation of households. Despite the deepest recession since the 1930s house prices still cost more than five times average salaries, well above the long-term average of 4.2.

Mark Clare, Barratt Developments' chief executive, says: "The risk is that we continue to see very low production volumes and increasing demand, which would lead to upward pricing pressure." He adds: "At the moment the housebuilding industry is around 40 per cent down on where it was. It took a very substantial step down and there is a limit to how far we can grow. It could be 2020 before the industry is back to where it was. That is where the risk is."

Housebuilders and construction firms made savage job cuts during the recession, leaving the sector employing almost 400,000 less staff than it did in the autumn of 2007. Two years of transition in the UK's painfully slow planning system, which culminated in the adoption of a new national planning policy framework and a presumption in favour of sustainable development, has meanwhile seen halting progress on planning permissions for new homes. According to figures prepared by construction consultants Glenigan for the Home Builders Federation, there were 33,881 between July and September last year, up 17 per cent on a year earlier but still well short of the 60,000 per quarter needed to meet demand, or the 64,500 being granted on average during the boom years of 2006/07. An HBF spokesman says: "We know there is pent-up demand. What we can't do is allow the constraints of the planning system to push up prices."

Pete Redfern, Taylor Wimpey's chief executive, adds: "It seems extremely unlikely that the level of planning permissions is going to increase significantly, while as the economy recovers there will be untapped demand emerging. It is difficult to see how that is not going to lead to house price increases."

The Council of Mortgage Lenders forecasts a £15bn rise in mortgage loans this year thanks to FLS, taking the size of the market to £156bn. This is still vastly below the 2007 peak of £362bn, but Bob Pannell, chief economist, says the body is "more positive" about the UK housing market. "A key reason is that lenders currently face few funding pressures, in part reflecting the FLS," Mr Pannell says.

As rents push to record highs due to the previous loan shortage, the economic argument is also tilting in favour of buying, with FLS bringing down lending rates and NewBuy helping buyers get over the deposit hurdle. In the second week of January, there was the highest number of reservations on record since the scheme began in March, at 123.

Some property economists are more sceptical over the danger of rising prices: the argument is that a buoyant new build market – around 10 per cent of the total – could be offset by the slack in the much bigger second-hand market as homeowners sitting tight until now due to lack of equity seize the chance to sell.

Daniel Solomon, housing economist at the CEBR research body, said: "FLS will probably have an impact but not enough to make credit skyrocket. London will be strongest because it has the strongest local economic growth and links with emerging markets, although the flow of 'hot money' flooding into London after the Arab Spring is likely to abate this year."

Mr Solomon adds that banks are too bogged down fighting against the twin shocks of the financial crisis and the eurozone's woes to fuel a housing boom with a huge surge in lending. "Either of those would have been big enough on their own," he adds. "We are living in a different world." Buyers frustrated for years by an inability to get on the housing ladder – as well as the Bank of England's inflation watchers – will hope he's right.