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Capital gains: London’s house price dilemma

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How high can London house prices go? You can hardly get on a bus or sit in a café in the U.K. capital without hearing an animated discussion about whether the city is no longer an affordable place in which to live.

Fuelled by record low interest rates and burgeoning consumer confidence in the U.K.'s economic recovery, the rise in house prices seems almost unassailable.

Around the U.K., house prices hit new records in May, according to the Nationwide index. The annual rise of 11.1 percent was the highest since June 2007 – just before the credit crisis hit.

And it is a relatively small part of the country – London and the South East - which is propping up the broader U.K. housing market.

In London, the top end of the market has been inflated partly by headline-grabbing investments from Russia, the Middle East and China. This has pushed wealthy local buyers out of Mayfair and Kensington to areas like Battersea, which saw rises of around 22 percent in 2013, according to estate agent Savills.

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In its annual assessment of the European Union economies, the European Commission became the latest to wade into the debate surrounding the UK housing market, by calling on the government to raise local council taxes on more expensive properties, build more houses and adjust the controversial Help to Buy scheme.

Help to Buy, where first time buyers' mortgages are guaranteed by the government, has so far been used by relatively few buyers, but may be more effective in helping to bolster expectations in the rest of the market. The scheme is playing a "supporting rather than a starring" role in the U.K. market at the moment, according to Nationwide, one of the U.K.'s biggest mortgage lenders.

"The scheme was designed to encourage high loan to value (LTV) lending.By the time it was introduced, lenders had already expanded their LTV terms, soit was answering a problem which was already being solved," Grainne Gilmore, head of UK residential research at Knight Frank, told CNBC.

Still, the potential for housing bubble history to repeat itself is not lost on policymakers or consumers. Expectations for house price rises have recently tailed off, according to estate agents Knight Frank.

Read MoreUK banks have to withstand 35 percent house price fall

Outside the glamorous world of Chelsea penthouses, there seems to be a serious lack of supply. A decade ago, a flagship report by respected government advisor Kate Barker warned that 260,000 new houses needed to be built annually to keep house price rises at around 1.1 percent. Since then, housebuilding has averaged 115,000 per year in the private sector, and only 6 percent of housebuilders in the U.K. believe it would be possible to build even 200,000 houses each year, according to Knight Frank.

In the long term, there are hopes that London may be commutable from cities like Manchester or Birmingham, once a planned high-speed rail link is introduced. Until then, house prices remain relatively moribund outside commutable distance of the capital.

Mortgage lenders are starting to tighten up their criteria as the point at which the Bank of England raises interest rates seems ever closer. The pressure on the Bank's policymakers to act to bring the market back to normality will only grow as a result.

Read MoreCarney: U.K. housing's deep problems

Domestic housebuilders are expected to be summoned by the Treasury chief George Osborne to a meeting to discuss how to stimulate construction in the coming weeks. With an election next year, it may be difficult for the governing Conservative Party to allow more building in the not-in-my-backyard London and the South East, its core constituencies. While construction PMI figures due Tuesday morning should show renewed confidence in the sector, the problem of how long it takes to get planning approval remains – and has not been helped by government cuts to local authority funding.

"U.K. housing is too expensive, yes. The solution is not to subsidise demand, but to build more houses," Robert Wood, chief U.K. economist at Berenberg, said.