As London sees house price growth soften to the weakest levels since 2012, the gap between the strongest-performing parts of the UK and the weakest has narrowed to four percentage points, Nationwide Building Society said.
The gap is the smallest since records started in the mid-1970s.
Average UK property values increased by 1.1% month-on-month in June, reversing monthly declines from the three previous months.
The increase pushed the average price across the UK to a new record of Â£211,301.
June's monthly increase was the strongest since a 1.2% uplift in April 2015.
Growth also accelerated on an annual basis, with a 3.1% increase in June, the strongest since March.
The East Anglia region has seen the strongest price growth annually, with a 5% uplift, followed by the South West at 4.4%, and the North West of England and the East Midlands with 4.1%.
The weakest annual growth was in the North East of England, which saw a 1.1% increase, followed by London at 1.2% and Wales with 1.4%.
In Scotland, prices increased by 1.7% annually, while in Northern Ireland saw growth of 3.8%.
Robert Gardner, chief economist at Nationwide Building Society, said UK-wide annual price growth has returned to the 3% to 6% range that had been prevailing since early 2015.
He said: "There has been a shift in regional house price trends. Price growth in the South of England has moderated, converging with the rates prevailing in the rest of the country.
"In quarter two the gap between the strongest performing region and the weakest was the smallest on record, based on data going back to 1974.
"London saw a particularly marked slowdown, with annual price growth moderating to just 1.2% - the second slowest pace of the 13 UK regions and the weakest pace of growth in the capital since 2012."
Mr Gardner said it is unclear whether the increase in June reflects strengthening demand on the back of healthy gains in employment and continued low mortgage rates, or whether the lack of homes on the market is the more important factor.
He predicted household spending is likely to slow in the quarters ahead, along with the wider economy, as rising inflation squeezes household budgets.
Mr Gardner said: "This, together with ongoing housing affordability pressures in key parts of the country, is likely to exert a drag on housing market activity and house price growth in the quarters ahead.
"However, the subdued level of building activity and the shortage of properties on the market are likely to provide support for prices. As a result, we continue to believe that a small increase in house prices of around 2% is likely over the course of 2017 as a whole."
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