LONDON—Costs are rising at the fastest rate in over 20 years for firms in Britain’s services sector, according to a business survey released on Tuesday which shows why the Bank of England may soon raise interest rates. The Confederation of British Industry said its quarterly survey of the services sector showed the quickest growth in costs for both business and consumer services companies since the survey began in 1998. Separate data from Lloyds Bank showed a record 50 percent of businesses plan to raise prices and a quarter of them expect to raise pay by 3 percent or more over the next 12 months. “Record growth in costs is threatening to put a winter freeze on the service sector recovery next quarter,” CBI economist Charlotte Dendy said. Both surveys took place in the first half of November, before news of the Omicron variant of COVID-19 dented the confidence of financial …