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* UK's stubborn inflation fails to fall in May

* Homebuilders hit on inflation data, Berkley's demand warning

* BNP Paribas cuts rating on NatWest, Llyods

* FTSE 100 down 0.3%, FTSE 250 off 0.8%

June 21 (Reuters) - UK's benchmark FTSE 100 fell to a three-week low on Wednesday, as inflation data deepened worries that the Bank of England (BoE) may need to tighten monetary policy even more, while Federal Reserve Chair Jerome Powell's testimony was also on tap.

The FTSE 100 shed 0.3% at 0800 GMT, while the FTSE 250 mid-cap index lost 0.8% after hitting an 11-week low.

After data showed consumer inflation was unchanged at 8.7% in May, contrary to expectations of a slight fall, traders assessed the possibility of a 50 basis points (bps) BoE rate hike on Thursday from the 25 bps hike anticipated earlier.

Concerns over the BoE's ability to bring inflation under control without tipping the economy into a recession weighed on sentiment.

"It is certain that the BoE's rate-hiking cycle is far from being close to its end, increasingly becoming an outlier compared to the Fed and ECB where the debate is more focussed on how close we are to seeing the terminal rate," said Stuart Cole, chief macro economist at Equiti Capital.

Homebuilders took the worst hit, falling 2.9% on concerns over elevated mortgage rates following the inflation data, and also dented by a 3.3% drop in Berkeley Group Holdings following a demand warning.

However, energy stocks gained 0.4%, tracking higher crude oil prices

Halfords gained 5.4% on plans to grow its bikes and car parts' market share to boost profits, while THG advanced 2.9% on expecting a significant increase in first-half profit.

Meanwhile, the banking sector was the biggest drag on the FTSE 100, with NatWest Group and Lloyds Banking Group losing over 1% each as BNP Paribas downgraded both the stocks.

Asset manager Liontrust fell 2.2% after reporting a lower annual profit, weighing on the investment banking and brokerage services index.

In a congressional testimony later in the day, Powell is poised to be questioned on the future of rate hikes by the world's most influential central bank. (Reporting by Ankika Biswas in Bengaluru; Editing by Sonia Cheema and Varun H K)