The Markit/Cips services purchasing managers' index (PMI) rose to 56.0. Any figure above 50 indicates growth.

Markit also reported the biggest monthly rise in business optimism since the survey started 15 years ago.

The data will reduce fears of a new recession, following a contraction in the economy at the end of last year.

An increase in new business also drove employment in the sector to rise at its fastest pace since March 2008, the survey found.

"All [this] points to a resounding revival of UK economic growth in January," said Chris Williamson, chief economist at Markit.

"A slide back into recession is now looking increasingly unlikely. The economy could well expand at close to trend rate - around 2-2.5% per annum - in the first quarter if business conditions hold up in the next two months," he added.

The data follows a similar survey showing the UK's manufacturing sector returned to growth in January, with overall activity at its highest level for eight months.

The results will be closely analysed by the Bank of England when it meets next week.

The Bank had been expected to expand its quantitative easing programme to provide extra credit to the economy.

However, the data contradicts the latest forecast from the National Institute of Economic and Social Research (NIESR).

The think tank predicted the UK economy would shrink by 0.1% in 2012.