The Purchasing Managers Index (PMI) shows that the capital was the strongest performer last month.
The index for London, based on a survey of 1,200 manufacturing and service sector firms, was at 60.6.
Any number above 50 is a sign that the economy is growing.
Across Britain output growth slowed in seven of the nine regions, with Yorkshire and Humber registering the weakest growth with a PMI number of 52.
The average figure for the whole of the country is 56.1, down from 57.6 in December.
The PMI survey is sponsored by England's Regional Development Agencies.
Mike Laverty, representing the agencies, said: "While the UK economy continues to recover, the unusually poor weather conditions experienced in January have contributed to a general easing in the rate of output growth.
"It is especially pleasing to see only modest falls in backlog and staffing levels.
"However, recovery remains fragile with the increase of VAT to 17.5 per cent and stronger input cost inflation squeezing profit margins."