LONDON, Sept 20 (Reuters) - The pound fell to its lowest since late May on Wednesday after data showed UK inflation slowed more than expected in August, softening the case for the Bank of England to raise rates much beyond current levels.

British annual consumer price inflation (CPI) unexpectedly fell to 6.7% in August, official data showed on Wednesday, a day before the BoE is expected to raise rates again.

Economists polled by Reuters had forecast CPI would rise to 7.0% from July's 6.8% after a jump in fuel prices and an increase in a tax on alcoholic drinks.

Sterling was last down 0.2% on the day at $1.2363, compared with $1.2386 right ahead of the data, having hit a session low of $1.2334 in the immediate wake of the report.

Investors scrambled to reel in bets that the BoE will raise interest rates again on Thursday. The overnight index swaps market pointed to a 45% chance that central bank will leave interest rates unchanged on Thursday, up from 20% on Tuesday.

The chances of further rate hikes that would take Bank Rate above 5.5% - priced as a certainty only a month ago - dwindled to around 20%, from above 40% on Tuesday.

"This slowdown of inflation may lead traders to become more cautious of the Bank of England following in the ECB's footsteps in hiking rates tomorrow as had been previously expected, although still looks to be the base case," Alex Livingstone, who is head of trading and FX at Titan Asset Management, said.

As recently as a month ago, money markets pointed to a peak in UK rates of close to 6% by next June, in light of evidence that inflation was becoming increasingly entrenched in the wider economy.

A STICKY SITUATION

Headline inflation is now at its lowest since February last year, while core inflation, which excludes food and energy prices, has proven far more stubborn, dropping to 6.2% in August, from 6.9% the previous month - at a five-month low.

Consumer price inflation is still running well over three times the BoE's target of 2% and Britain still boasts the highest rate of inflation among major economies.

"This was always going to be an important UK CPI figure immediately ahead of tomorrow’s Bank of England figure – after all, remember what happened in June when the May print came out super-strong and the BoE hiked by 50 basis points, rather than the 25 basis points that had been expected?" Nomura economist George Buckley said.

"Now we have exactly the opposite situation – might a huge downside miss stop the Bank of England from another hike? This is now a very real risk indeed, especially with pretty much all the data we’ve seen between the August and September MPC meetings being weaker," he said. (Reporting by Amanda Cooper; Editing by Harry Robertson and Toby Chopra)