The IHS Markit/CIPS UK services Purchasing Managers' (PMI) dropped to 47.6 in November from 51.4 in October, the first time since June that it fell below the 50 level that divides growth from contraction.
But this was a much smaller decline than during the first lockdown in April, when the PMI hit a record-low of 13.4, and less of a slowdown than an earlier 'flash' November reading of 45.8.
The composite PMI, which includes manufacturers who enjoyed stronger growth, dropped to 49.0 from 52.1.
News of effective COVID-19 vaccines also boosted business optimism in the services PMI, which rose to its strongest since February's five-year high.
Samuel Tombs, an economist at Pantheon Macroeconomics, said the downturn could still prove significant, as a separate survey from Britain's Office for National Statistics pointed to a hefty 3% monthly drop in revenue in early November.
"We still look for around a month-to-month drop in GDP of about 5% in November, followed by an incomplete rebound of around 4% in December," he said.
Britain's economy suffered a record 25% fall in output in March and April. The Bank of England forecast this month that output would fall just 2% in the final three months of 2020.
Thursday's PMI survey showed job losses continued for a ninth consecutive month, the longest run since 2010.
Unemployment is forecast to rise further during the months it will take to roll out the vaccine to millions of Britons.
While some sectors such as retail - which is not covered by the PMI - and hospitality have been hard hit by the second lockdown, others have found it easier to adapt, IHS Markit said.
A Bank of England (BoE) survey showed optimism for 2021. Businesses expected sales in the second quarter of 2021 would be only 2% below pre-pandemic levels, less severe than an 8% shortfall forecast a month earlier.
The services PMI survey took place from Nov. 12-26, while the BoE survey was conducted from Nov. 6-20, meaning most responses came after news of the initial COVID-19 vaccine breakthrough from Pfizer and BioNTech on Nov. 9.
Businesses that traded with the European Union also told the BoE they were more prepared for new post-Brexit customs requirements from Jan. 1. - though almost a third said they were still only partly or not at all prepared with just weeks to go.
(Reporting by David Milliken; Editing by Hugh Lawson and Mark Potter)
By David Milliken