ISTANBUL, Nov 3 (Reuters) - Turkish annual inflation climbed to a new 24-year high of 85.51% in October, official data showed on Thursday, slightly below forecast, after the central bank cut its policy rate despite surging prices.Inflation has surged since last year, when the lira slumped after the central bank began cutting its policy rate in an easing cycle long sought by President Tayyip Erdogan.Haluk Burumcekci, founder of Burumcekci Consulting, said the October print could be the peak for headline inflation if the lira does not weaken further.Month-on-month clothing led the price rises with 8.34%, followed by food prices, which rose 5.09%, and furnishing and household equipment prices, which rose 4.38%.The government's economic programme prioritises low rates to boost production and exports with the aim of achieving a current account surplus."