(Reuters) - London stocks rebounded on Wednesday on revived hopes of interest rate cuts in the near future after data showed cooling inflation in the U.S. and a slowing economy in Britain, while Rentokil Initial further added to the gains.

The blue-chip FTSE 100 closed 0.8% higher in its best day in over a month, while the mid-cap FTSE 250 was up 1.1%, snapping a three session losing streak.

A key U.S. government report showed consumer prices did not rise at all in May, with traders adding to bets of an interest rate cut in September by the Federal Reserve.

The benchmark U.S. S&P 500 rose over 1%, while the tech-heavy Nasdaq Composite Index hit a record high after the data. [.N]

Meanwhile, British data showed that economic output was flat in April and the rebound in the economy came to a halt.

"Signs that the UK economy's recovery has stalled added to expectations that the BoE could cut interest rates sooner. The prospect of the Fed also cutting sooner is helping global sentiment," said Fiona Cincotta, senior market analyst at City Index.

In the London market, the industrial support sector gained 3.7%, leading a broader rally. Rentokil Initial surged 13.7% to top the FTSE 100, after Bloomberg News reported that Nelson Peltz's Trian Fund Management has amassed a significant stake in the pest-control firm.

Investors are now bracing for the Federal Reserve's next monetary policy decision, due later in the day.

Cincotta also pointed that if there was "an increasing sense" that the BoE and the Fed were moving close to their rate cutting cycle, it could help the FTSE 100 over the crucial 8,200 level, depending on "what we hear from the Fed this evening."

In corporate news, life insurer Legal & General lost 5.5% after planning a 200 million pound ($254.9 million) share buyback and a merger of its investment units.

Molten Ventures was the top gainer on the mid-cap index, with a 19.1% jump, after the venture capital firm reported its final-year results.

(Reporting by Pranav Kashyap and Purvi Agarwal in Bengaluru; Editing by Sonia Cheema and Hugh Lawson)

By Pranav Kashyap and Purvi Agarwal