July's survey had shown a steep drop in business activity in the immediate wake of the referendum, but that started to recover in August.
Chris Williamson, chief business economist at IHS Markit, which compiles the survey, said: "The survey results suggest the economy has regained modest growth momentum since the European Union referendum, with further service sector expansion accompanied by a return to growth in construction and an especially strong revival of manufacturing". Construction companies pointed to a renewed rise in civil engineering activity, with the pace of expansion the fastest since March.
Sector activity was buoyed over the period by the rise in new work for the first time since April, which was driven in part by growing demand from the housing market.
Markit economist Oliver Kolodseike said the German services sector was in a waiting position, adding that weaker growth in new orders and lower levels of business outstanding raised the spectre of a weak performance in the coming months. This in turn led to a further moderate rise in employment levels across the construction sector, although sub-contractor usage continued to fall at one of the fastest rates since late-2013.
"The ongoing upturn in new work combined with muted employment growth led backlogs of work across the private sector to increase at the quickest pace in almost two-and-a-half years", De Lima said.
Samuel Tombs, chief United Kingdom economist at Pantheon Macroeconomics, said he remained cautious over the prospects of a slowdown in services because of an increase in cost pressures.
Aqib Talib could still face discipline over shooting
Talib has played in all four games for the undefeated Broncos this season and has three interceptions and one defensive touchdown. To this point, Talib has offered few specifics on the incident other than "I want to move on and concentrate on the season".
It came as JP Morgan upgraded its forecast for United Kingdom growth for the second time in as many months.
The positive survey data helped the pound to pare some of its losses against the dollar after falling close to a 31-year low early on Monday.
She said that food and petrol prices continued to climb in September, which placed pressure on operating costs.
Services business activity index softened slightly in September to 52.6 after rebounding to 52.9 in August from 47.4 in July.
The Office for National Statistics (ONS) revised up its reading for the United Kingdom economy last week, with GDP growing 0.7% in the second quarter, up from a previous estimate of 0.6%.
UK GDP grew by 0.4% in the first three months of the year.