The index hit 52.1 points, compared to 40.2 in September, according to a report by research company IHS Markit. A reading above 50 indicates growth in manufacturing.
"Renewed expansions were seen for output, new orders and purchasing activity, while business confidence jumped higher."
A loosening of Covid-19 restrictions led a number of firms to restart production in October, while others expanded output in response to higher new orders.
Business confidence improved markedly in October as the latest wave of the Covid-19 pandemic showed signs of easing. Hopes that the pandemic would remain under control helped optimism reach a 29-month high.
But issues around staffing levels remained despite the wider return to growth.
Employment continued to fall markedly in October, with a number of firms indicating that some of their staff members had returned to their hometowns during the latest wave of the pandemic and had yet to return to their place of work.
"The problems with transportation and supply chains haven't gone away, making the sourcing and distribution of products challenging," said Andrew Harker, economics director at IHS Markit.
Input costs increased at the fastest pace since April 2011 and at one of the sharpest rates in the survey's history, the report noted.
Efforts to guard against likely future price rises encouraged firms to expand their input inventories for the third month running in October, it added.