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Updated at 1540 GMT

By Khushi Singh

Aug 30 (Reuters) -The UK's main stock index hit over a three-month high on Friday, clocking gains for the topsy-turvy month, with real estate shares in the lead as interest rate-cut hopes held firm, while energy shares tumbled on demand concerns, capping intra-day gains.

The blue-chip FTSE 100 index .FTSE ended flat, but registered its second straight monthly gain and third consecutive weekly advance.

The FTSE 250 .FTMC, which tracks mid-cap UK companies, rose by 0.3%, but declined over the past week and month.

The U.S. Personal Consumption Expenditure index, the Federal Reserve's preferred inflation gauge, rose 2.5% in July on an annual basis compared with an estimate of 2.6%, according to economists polled by Reuters.

Inflation in the euro zone fell to its lowest level in three years in August, setting the stage for a further cut in the European Central Bank's rates next month.

Rate-sensitive real estate investment trusts .FTNMX351020 added 1.6% through the day, while real estate .FTUB3510 shares gained 1.5%, leading sectoral gains.

The oil and gas .FTNMX601010 index was the bottom performer, slipping 1.1% as concerns about demand and the prospect of bigger supply from OPEC+ weighed on crude prices. O/R

Precious metal miners .FTNMX551030 also lost 1.1% following softer gold prices as the U.S. dollar and Treasury yields firmed after U.S. inflation data matched expectations. GOL/

In individual stocks, Anglo American AAL.L signed agreements with Chinese fertiliser companies Sinochem Fertiliser and BeiFeng AMP to develop the market for polyhalite fertiliser products in China, even as it slowed the development of its mine for the mineral in northern England. The miner was down 1.3%.

August marks a turbulent month for financial markets globally as concerns over a likely U.S. recession rocked risky assets. However, relief trickled in eventually as the Federal Reserve hinted at an imminent rate cut.

Meanwhile, British house prices unexpectedly fell in August for their first monthly drop since April but the outlook for the property market is likely to strengthen.

Reporting by Khushi Singh, Ankika Biswas in Bengaluru; Editing by Sonia Cheema and Jonathan Oatis

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