The annual growth rate has slowed since mid-2016 following the European Union referendum, from a high of 8.2 per cent in June previous year at the time of the vote.
Average house prices in the UK increased by 4.9% in the year to June 2017, down from 5.0% in the year to May 2017, according to the latest UK HPI.
Despite slower increases in the value of property, first-time buyers are still entering the market, according to data published separately on Tuesday by the trade body UK Finance.
In Dudley it was up 3.1 per cent to £160,041, in Sandwell the average price rose 4.1 per cent to £133,915 and in Walsall it was up 3.1 per cent to £152,314.
The average price of a home in the United Kingdom went up by almost £2,000 to £223,000 in June, according to official figures. There was similar growth, of 7.1pc, in the East Midlands.
In Scotland, the average price increased by 2.9% over the year to stand at £144,000.
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In the month of June, the average price of London home fell £3,000 to £482,000, while a house in the North East of England gained £2,000 to £130,000.
"There is a degree of inevitability about prices cooling, as house price inflation in the capital raced ahead of wage inflation for several years, but ultimately this situation was always going to be unsustainable".
In June, the most expensive borough to live in was Kensington and Chelsea in London, where the average cost of a house was £1.4m.
Word on the ground, from north London estate agent Jeremy Leaf, a former RICS residential chairman, was that the Land Registry figures: "show a fairly stable market at a time when we might have expected more nervousness among buyers and sellers".
Last week, the Royal Institution of Chartered Surveyors said its members believed prices had stood still on average in recent months and that a slowdown was spreading from London to other parts of the South East of England.
"The fact that inflation has fallen from 2.9% to 2.6% and is staying there is good news for the housing market as expenditure won't feel any more squeezed than it has done over the past few months and may even persuade some to take the plunge".
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