LONDON—The dollar fell further on Thursday to two-month lows after U.S. inflation proved weaker than feared in December, prompting investors to cut crowded long positions in the currency. The euro was a big beneficiary of the move and extended its rise to as high as $1.1479, up 0.3 percent on the day, while sterling and the yen also added to their gains. December’s monthly U.S. inflation figures, published on Wednesday, were a fraction higher than forecast and the increase in year-on-year consumer price inflation was as expected at 7 percent—its biggest jump since June 1982. Nevertheless, traders do not see these inflation readings as urgently shifting an already hawkish Federal Reserve too much. With at least three rate hikes already in the market price, some investors pared bets on further dollar gains. The dollar index, which measures the greenback against a basket of rival currencies, fell another 0.2 percent to …