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* FTSE 100 up 0.4%, FTSE 250 adds 0.6%

* Real estate stocks gain after Nationwide industry report

* British parliamentary elections in focus

July 1 (Reuters) - London stocks kicked off the week on an upbeat note, supported by real estate shares and tracking gains from the European market amid a revival in hopes of rate cuts globally.

The blue-chip FTSE 100 was up 0.4%, on track to snap a four-session losing streak. The mid-cap FTSE 250 was up 0.6% at 0730 GMT.

Over the weekend, the first-round voting in France's shock snap election was won by the far right.

"There's just optimism that maybe the French election didn't pan out so far as badly as feared. And that's lifted the mood across (the continent)," said Fiona Cincotta, senior market analyst at City Index.

"We've also got that optimism stemming from Friday's US core PCE and that the Federal Reserve might start cutting interest rates sooner."

The personal consumption expenditure report in the U.S. on Friday showed that inflation was in line with expectations.

The pan-European STOXX 600 was last up 1.1%.

In the London market, real estate stocks were among the top gainers with a 1.2% rise after a Nationwide report showed British house prices showed a small gain in June from May but the impact of higher interest rates still weighed on the property market.

Real estate investment trusts (REITs) gained 1.3%.

Britons are headed towards the domestic parliamentary elections on Thursday, which opinion polls suggest will see Labour Party leader Keir Starmer replace Conservative Rishi Sunak as prime minister.

In corporate news, Anglo American slipped 3.2% to the bottom of the FTSE 100 after the miner said it had suspended production at its Australian metallurgical coal mine after an underground fire ignited there on Saturday.

(Reporting by Purvi Agarwal in Bengaluru; Editing by Mrigank Dhaniwala)