By David Milliken LONDON (Reuters) – Activity in Britain’s private sector picked up at the fastest pace since June 2021 this month, as spending on travel, leisure and entertainment rose after an easing in the Omicron wave of coronavirus cases, a survey showed on Monday. However, businesses’ costs rose at the second-fastest rate since the IHS Markit/CIPS composite Purchasing Managers’ Index (PMI) began in 1998, which will add to the Bank of England’s (BoE) concerns about the persistence of soaring inflation. The composite PMI’s headline output index rose to 60.2 in February from 54.2 in January…