By David Milliken LONDON (Reuters) – British private-sector growth slowed to its weakest pace in four months in April as businesses raised prices on the broadest basis since at least the late 1990s, a closely watched survey showed on Thursday. The figures from the S&P Global/CIPS Purchasing Managers’ Index (PMI) highlight the challenge facing the Bank of England, which is widely expected to raise interest rates later on Thursday as it seeks to tame inflation while minimising the chance of a longer-term slowdown. “The twin headwinds of the cost of living crisis and the war in Ukraine started to…