* Challenge on "hard Brexit" stokes buying on UK government debt * U.S. core CPI rises 0.1 pct, less than forecast * Dealers sell Treasuries to hedge large Saudi bond issue (Recasts with updated market action; adds quote) By Richard Leong NEW YORK, Oct 18 (Reuters) - U.S. Treasury yields fell on Tuesday in line with their U.K. counterparts on chances that parliament may have to ratify a British exit from the European Union, which reduced some bets that the U.K. would lose access to the single market. U.S. bond yields pulled further away from four-month peaks set on Monday on data that showed the underlying inflation trend moderated in September. This revived expectations it may take longer than previously thought for domestic inflation to reach the Federal Reserve's 2 percent goal, keeping the Fed on a glacial path on raising interest rates. "The initial strength came from gilts," said Jim Vogel, interest rates strategist at FTN Financial in Memphis, Tennessee. "The inflation trade which has come in bursts has cooled a bit," he added. A lawyer who represents the U.K. government in its challenge over who has the right to trigger Brexit divorce talks, James Eadie, said parliament would "very likely" have to ratify any Brexit agreement. This runs counter to Prime Minister Theresa May's hard line for a rapid exit from the EU. A hard Brexit is seen among some investors as harmful to the British economy, making gilts less attractive. Uncertainty on how London's High Court may rule stoked some buying of U.K. government debt with 10-year yields falling over 4 basis points to 1.077 percent. Benchmark U.S. 10-year Treasury notes were last up 4/32 in price for a yield of 1.750 percent, down 1.6 basis points and not far below a four-month peak of 1.841 percent reached on Monday. Treasury yields briefly rose earlier on Tuesday as dealers sold government bonds to hedge a large global bond issue from Saudi Arabia that they are underwriting. Saudi Arabia planned to sell a multi-part bond issue worth $10 billion to $15 billion, according to IFR, a Thomson Reuters unit. Bond dealers typically sell Treasuries to hedge against a deal they underwrite and then buy them back after the deal is sold. The U.S. Labor Department said on Tuesday the Consumer Price Index, its broadest inflation gauge, rose 0.3 percent in September, matching the median forecast among analysts polled by Reuters. However, the CPI core rate, which excludes volatile food and energy prices, edged up 0.1 percent in September, falling short of an expected 0.2 percent increase. Tuesday, Oct. 18 at 1437 EDT (1837 GMT): Price US T BONDS DEC6 164-9/32 0-11/32 10YR TNotes DEC6 130-80/256 0-48/256 Price Current Net Yield % Change (bps) Three-month bills 0.3425 0.3476 0.000 Six-month bills 0.4725 0.4802 0.002 Two-year note 99-230/256 0.8026 -0.020 Three-year note 100-30/256 0.9601 -0.021 Five-year note 99-124/256 1.2327 -0.023 Seven-year note 98-248/256 1.532 -0.024 10-year note 97-196/256 1.7485 -0.018 30-year bond 94-120/256 2.5147 -0.008 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 22.50 0.50 spread U.S. 3-year dollar swap 14.00 0.25 spread U.S. 5-year dollar swap 1.75 0.25 spread U.S. 10-year dollar swap -17.00 0.00 spread U.S. 30-year dollar swap -56.75 -0.25 spread (Reporting by Richard Leong; Editing by Nick Zieminski and Leslie Adler)