LONDON, June 1 (Reuters) - Hedge funds cut their bullish positions in petroleum last week for the third week running, though the rate of selling was slower than in previous weeks and positions are broadly unchanged since the middle of March. Hedge funds and other money managers sold the equivalent of 8 million barrels in the six most important petroleum futures and options contracts in the week to May 25, according to exchange and regulatory reports. Small sales in Brent (-12 million barrels), U.S. gasoline (-6 million) and European gas oil (-6 million) were partly offset by small buying in NYMEX and ICE WTI (+10 million) and U.S. diesel (+6 million).