The latest Markit/CIPS services Purchasing Managers' Index (PMI) fell to 52.7 last month, down from January's reading of 55.6.
Any figure above 50 means expansion, but the rise in service sector activity was the weakest since March 2013.
The service sector accounts for more than three-quarters of the UK economy.
Surveys from Markit/CIPS earlier in the week put the manufacturing sector's PMI at 50.8 and construction at 54.2.
"The weaker increase in services activity mainly reflected a slower expansion in the volume of incoming new business," the survey said.
Markit chief economist Chris Williamson added: "Survey responses reveal that firms are worried about signs of faltering demand, but boardrooms have also become unsettled by concerns regarding the increased risk of 'Brexit', financial market volatility and weak economic growth at home and abroad."
He added that the extent of the slowdown would come as a "shock" to policymakers and would put an end to talk of a possible interest rate rise.
Mr Williamson described February's three PMI readings as "a triple whammy of disappointing survey news".
Last week, official figures confirmed that the UK economy grew 0.5% in the final three months of 2015, with the services sector highlighted as the key factor driving growth.
The Office for National Statistics said the "buoyancy" of services had offset the "relative sluggishness" of the rest of the UK economy.
Signs of weakening growth in the UK economy have pushed back estimates of when the Bank of England might begin to raise interest rates.
Commenting on the latest PMI survey, Jeremy Cook, chief economist at World First, said: "The May Bank of England meeting had previously been seen as a possible time for a rate hike. The volatility of global markets and the self-inflicted wound of the EU referendum put paid to that months ago.
"We still believe, however, that some measures that foresee the Bank of England holding rates at 0.5% until 2020 are little short of absurd."
Martin Beck, senior economic adviser to the EY Item Club, said the PMI readings would provide "plenty of food for thought" for the Bank of England's rate-setting Monetary Policy Committee.
He added: "Members will have to judge the degree to which the surveys are flagging a genuine slowdown in activity growth, or merely reacting to the negative headlines since the start of the year. In reality, growth may be softening, but perhaps not as sharply as the survey data suggest."
Meanwhile, a similar survey indicated that eurozone businesses had their worst month for more than a year in February, bolstering the case for more monetary policy easing by the European Central Bank.
Markit's final composite PMI, which is regarded as a good guide to growth, fell to 53 last month from January's 53.6 - its lowest reading since the start of 2015.
However, that was better than the preliminary reading of 52.7 and well above the 50 mark that denotes growth.
The UK's dominant services sector weakened in February, registering its slowest rate of growth for nearly three years, a survey has indicated.