The 'flash' or preliminary reading of the S&P Global/CIPS UK Composite Purchasing Mangers' Index (PMI) - spanning services and manufacturing firms - came in at 52.2 in March, down from 53.1 in February but above the 50 threshold for growth.
Economists polled by Reuters had forecast a reading of 52.8.
Bank of England Governor Andrew Bailey said in an interview broadcast on Friday that he expected Britain would now avoid recession this year, although growth prospects remained subdued.
Retail sales data also released on Friday showed stronger-than-expected growth for February and January - though Britain's Office for National Statistics said this could reflect cash-strapped households cutting back on takeaways and restaurant meals in favour of eating at home.
Many businesses and households are still feeling squeezed.
While the services PMI was in positive territory at 52.8, the manufacturing survey slipped to 48.0, representing its eighth month of contraction.
Firms across the two sectors were more optimistic about their prospects over the next 12 months, with the degree of confidence hitting its highest since March 2022.
S&P Global said this improved confidence largely reflected an easing of post-COVID supply chain difficulties in the manufacturing sector and stronger customer demand.
"With the flash PMI surveys signalling a second month of rising output in March, the UK economy looks to have returned to growth in the first quarter," S&P Global's chief business economist, Chris Williamson, said.
There was an even bigger upturn in the euro zone, where the composite PMI rose to a 10-month high of 54.1 from 52.0.
"An upturn in companies' expectations for the year ahead indicates that business sentiment has been little affected so far by the banking sector woes and that firms are more focused on growth possibilities," Williamson said, of the situation in Britain.
While the rate of growth in the services industry slowed this month compared to February, new business activity rose at the sharpest pace in 12 months. Manufacturing output fell marginally as subdued demand depressed volumes.
Friday's survey added to a series of improved measures of the UK economy which had appeared to be heading for a recession in early 2023, although on Thursday the BoE said it still expected it to shrink in the January-March period before picking up in the second quarter.
Official data published earlier in March showed the economy unexpectedly returned to growth in January.
A GfK survey of British consumer sentiment on Friday was the strongest in a year, though still weak by historic standards.
Gabriella Dickens, senior UK economist at Pantheon Macroeconomics, said widespread public-sector strikes in the first quarter of 2023, as well as the impact of higher interest rates on construction, could still lead to a fall in gross domestic product in the first quarter.
"The risk of a tightening of credit conditions also looms over the near-term outlook," she said.
Although the collapse this month of the United States' Silicon Valley Bank and UBS's takeover of flailing Credit Suisse has had little direct impact on most British businesses, the BoE said these problems had pushed up British lenders' financing costs.
S&P Global's input price index - a good guide of future inflation pressures - showed growth in costs for firms falling to the lowest since April 2021, although overall cost pressures remained high by historical standards.
Service firms flagged a steeper rise in input prices than manufacturing companies, with the latter recording the slowest increase since June 2020.
Companies said lower fuel bills and transport costs, partly offset wage pressures and higher food prices.
The BoE on Thursday increased interest rates to 4.25% from 4% after a surprise surge in consumer price inflation which hit 10.4% in February. But some economists said the hike might be the last in a run of rate hikes going back to December 2021.
Financial markets expect one more BoE rate increase, to 4.5%, in the coming months.