The Markit/CIPS Purchasing Managers' Index (PMI) for the service sector rose to 52.1 in November from 51.3 in October, beating expectations for a dip to 50.5 and edging higher above the 50 mark that separates growth from contraction. The index was still below September's reading of 52.9 however.
Britain's economy as a whole looks likely to barely grow in the final three months of 2012, after PMI surveys last week showed sluggish construction activity and the biggest fall in manufacturing since June 2009.
"With manufacturing contracting at a steep pace, the weak growth of services means the economy is likely to have stagnated in the fourth quarter," said Chris Williamson, chief economist at data provider Markit.
The Organisation for Economic Cooperation and Development has warned that Britain is entering a modest recession, while the government has said the economy will stagnate until mid-2012 and could easily start to contract.
The pick-up in activity in services was driven by a continued inflow of new business - albeit at the slowest rate since December 2010 -and by extra advertising and marketing, the purchasing managers' survey showed.
By sub-sectors, activity increased in the business-to-business services sector but declined in IT and computing, and transport, storage and communications categories. The survey does not include retailers or public services.
Brisker business did not translate into safer job prospects, however. The employment sub-component fell to 48.2 from 49.8, showing the biggest drop in the workforce in 15 months, both through redundancies and natural attrition. Job losses were heaviest for hotels, catering and restaurants, and for transport, storage and communications.
Manufacturing firms, too, cut jobs at the fastest rate in more than two years, signalling that the rate of unemployment in Britain is likely to rise above the 15-year high of 8.3 per cent recorded in the three months to September.
Services firms blamed a tough economic climate, the euro zone debt crisis, low bank lending and public spending cuts for depressing growth.
The uncertain environment also weighed on business confidence, which slipped from October's five-month peak.
Companies' profit margins were pressured by higher input costs, as utility bills and transport costs rose, while their ability to pass these on to clients was limited by discounting and the need to stay competitive.