Recruitment firm Reed said jobs had risen by almost a quarter over the past year, with almost 8,000 new posts added to its website in one day last month.
Vacancies in manufacturing and retail were said to be particularly buoyant - up by almost a third compared with a year ago - although the best performing sector was construction, with a 78% increase, said Reed.
But pay remained the same as a year ago and was 4% lower than four years ago.
James Reed, chairman of reed.co.uk, said: "Our vacancy figures have indicated an improving picture of the state of the UK economy since before the beginning of 2013.
"While previously growth was being driven by a handful of sectors and locations, encouragingly September saw jobs growth across the vast majority of sectors and across all regions.
"Amidst all the positive indicators, the absence of salary growth continues to temper wider optimism. Pay has remained static for the past three months now and our figures show that since our index began in 2009, employees won't have noticed an improvement in their pay packets.
TUC general secretary Frances O'Grady said: "Vacancies may be rising but unemployed people still outnumber jobs by around five to one across the country.
"All new vacancies are welcome, but with four in five new jobs created in industries where the average wage is just £8 an hour, people are still struggling to make ends meet in this low-pay recovery.
"We need better new jobs to start lifting people's incomes and give Britain a pay rise."