The Office for National Statistics (ONS) said manufacturing output rose by 0.6% in September, up from 0.2% in August and above July's sharp fall of 0.9%.
However, industrial production dropped by 0.4% in September, with economists pencilling in flat growth.
For the third quarter, covering the first three months since the EU referendum result, manufacturing and industrial production fell by 0.9% and 0.5% respectively, compared with the quarter before.
ONS statistician Kate Davis said: "Manufacturing was broadly flat across the third quarter while oil and gas were weak overall, with widespread summer maintenance shutdowns hampering production more than usual.
"There are no obvious signs so far of either the weaker pound or post-referendum uncertainties affecting the output of UK factories, which continued broadly in line with recent trends."
The ONS said the biggest boost to manufacturing output month-on-month came from manufacturing and other repair, rising 3.6%.
This was driven by a 8.5% rise from the rest of the repair and installations sub sector, which includes the repair of fabricated metals and the repair of machinery.
However, industrial production output was dragged down in September by a 3.8% drop in mining and quarrying, with oil and gas extraction sliding 4.5%.
Howard Archer, chief UK and European economist at IHS Global Insight, said despite stepping up a gear in September, the manufacturing industry is facing a bumpy road ahead.
"There are significant potential problems for the sector that look likely to build up in 2017.
"In particular, business confidence is likely to be hampered by mounting uncertainty over the Brexit process, constraining investment plans and limiting demand for capital goods."
The update from the ONS comes after the closely-watched manufacturing purchasing managers' index (PMI) showed that the industry remained on a firm footing in October.
Output held steady as sterling's near-20% fall against the US dollar since the Brexit vote boosted export opportunities.
However, it said the currency weakness had also ramped up import prices and the cost of products linked to dollar-denominated commodities such as oil.
Official figures revealed last month that the UK economy bucked expectations of a substantial slowdown in the three months after the Brexit vote thanks to a ''strong performance'' from the powerhouse services sector.
The ONS said gross domestic product (GDP) grew by 0.5% in its first estimate of third-quarter growth, down slightly from 0.7% in the second quarter, with economists pencilling in a steeper fall to 0.3%.
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