LONDON—British businesses grew at the slowest pace since April 2021 during the past three months, after demand for face-to-face services slumped due to the Omicron variant of coronavirus, the Confederation of British Industry said on Sunday. Britain’s economy only recovered to its pre-pandemic size in November, before being hit by the highly infectious Omicron variant which led to government advice to work from home and restrictions on hospitality in Scotland and Wales. “Consumer services have borne the brunt of ‘Plan B’ restrictions and general Omicron caution, with activity here shrinking sharply,” CBI economist Alpesh Paleja said. The CBI’s monthly growth index—which is based on quarterly growth rates from its previously published surveys of manufacturers, retailers, and other services businesses—fell to +12 in January from +21 in December. That was the lowest reading since April, which covered a three-month period when pubs, restaurants, and non-essential retailers were largely closed due to …