The closely watched Markit/CIPS UK Manufacturing purchasing managers' index (PMI) said output hit 55.4 last month, up from 53.4 in August, and above economist expectations of 52.1. A reading above 50 indicates growth.
The move means output hit its highest level since June 2014 in September and shows a marked improvement since it dropped to 48.3 in July after the Brexit vote.
Rob Dobson, senior economist at IHS Markit, said: "The rebound over the past two months has been encouragingly strong, and puts the sector on course to provide a further positive contribution to GDP in the third quarter."
Conditions in the manufacturing sector brightened towards the end of the third quarter, with growth accelerating for output and new orders, the report said.
Output rose at its quickest in one-and-a-half years in the consumer goods sector, while manufacturing production saw its fastest expansion since May 2014.
New orders were also on the rise in domestic and overseas markets, with the fall in the value of the pound against the US dollar and the euro since the Brexit vote helping export sales to expand.
It said the level of incoming new export orders rose at its fastest pace since January 2014 amid a growing appetite for British products from America, Europe, Asia and some emerging markets.
Dobson said: "The weak sterling exchange rate remained the prime growth engine.
"The domestic market is also still supportive of growth, especially for consumer goods. Further step-ups in growth of new business and output in the investment goods sector may also be a sign that capital spending is recovering from its early-year lull, in the short term at least."
September's performance means manufacturing output recorded a third-quarter average of 52.3 - its best reading for the year.
Employment levels in the industry also rose for the second month in a row despite falling earlier this year.
James Knightley, senior economist at ING, said the bounce back in manufacturing PMI "casts serious doubt" over the prospect of additional monetary policy easing from the Bank of England in November.
The pound pared losses to a fall of 0.6% against the US dollar at 1.288 US dollars following the PMI announcement.
Sterling also clawed back ground against the euro to drop 0.5% to 1.147 euros.
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