Prices rose 1.8 per cent last month, according to the figures released by Halifax, following May's increase of 2 per cent.
"This the first time we have had back-to-back rises of between 1.5 per cent and 2 per cent since 1988," said a spokesman for the bank.
The increase takes the annual rate to 6.6 per cent, almost 1 per cent up on the 5.7 per cent recorded in May.
However excluding homes sold to first-time buyers, prices are rising at 6.9 per cent - their highest rate of increase since October 1989.
The figures come in the same week that data from Nationwide, the UK's largest building society, showed house price inflation accelerated in June. Prices rose 7.5 per cent this month, compared with 7.4 per cent in May and 7.1 per cent in April, the Nationwide said. Halifax was anxious to play down fears of another housing boom, saying that people should wait for a six-month trend to emerge.
"The housing market is being driven by strong gains in the south of England, particularly Greater London, where a shortage of quality properties has created localised hot-spots," it said. "Price growth in the rest of the UK remains subdued. We expect rising unemployment will start to dampen housing demand over the next 12 months."
Halifax said there was "no evidence" to suggest a return to the boom times of the late Eighties, pointing out the transaction volumes were well below 1988-levels. It said the market was underpinned by historically low mortgage rates and favourable affordability.
Last month Halifax raised its forecast for 1999 by 50 per cent to 6 per cent from 4 per cent.Reuse content