The average house price paid by first-time buyers rose by 6.4% in the year to November, a faster rate than the market generally, official figures show.

The Office for National Statistics said that new entrants to the housing market paid an average of £187,000 during the month – £14,000 more than in the same month of 2012. The average price paid by movers was higher, at £284,000, which was 5.3% up on 12 months previously, while the average increase across the board was 5.4%.

First-time buyers have been assisted by the government's Help to Buy scheme, which has made properties available to those with just a 5% deposit to put down, and lenders' increasing willingness to offer high loan-to-value (LTV) mortgages.

However, the figures show that as the mortgage market becomes more accessible, prices are being driven up.

Surveyors and estate agents have said that a lack of supply of homes for sale is putting pressure on prices, and the second part of the Help to Buy scheme, launched in October, has been criticised for increasing demand without encouraging builders to provide new homes.

The ONS figures showed growth across the UK, with England recording a 5.6% rise, Wales a 5.4% increase, Scotland 2.5% and Northern Ireland 3.3%.

London and the south-east continued to drive the headline figures, with the capital seeing a 11.6% increase year-on-year, taking average prices to £441,000, and the rest of the south-east growing by 4.5% to an average of £216,000.

If the latter areas are stripped out of the UK figures, prices are up by 3.1% at an average of £194,000 – £54,000 lower than the headline average.

Richard Sexton, director of e.surv chartered surveyors which carries out valuations for more than 25 lenders, said prices were being pushed up "artifically quickly" by the lack of new homes on the market.

"First-time buyers are bearing the brunt of this rise. They are being forced to scramble over the small supply of affordable properties left, and all the while rising prices are driving their monthly repayments higher," he said.

"We desperately need more construction in order to prevent the bottom of the market being priced out entirely. In particular, we need more house building in London and the south-east – where demand, and prices, have risen the fastest."

Brian Murphy, head of lending at the Mortgage Advice Bureau, said price rises would mean more buyers turning to high LTV mortgages.

"As a growing number of lenders sign up to the government's Help to Buy 95% mortgage scheme, it's likely that mortgage activity will rise even further in 2014," he said. "Additional house price growth makes 95% mortgages even more of a valuable tool for the house buying public."

Research by the property website Zoopla suggests that UK homeowners are expecting more price increases in 2014, with 7,796 respondents to a survey predicting an average rise of 7.2% by the summer.

Those in London anticipate the biggest growth, predicting a 9.6% increase by June, but even in areas which have seen a slower recovery homeowners expected rises of at least 5.5%.