Forty workers have been made redundant at Nelson Packaging's factory in Lancashire.
Managing director Michael Flynn said it was mainly due to "the English bag legislation and corresponding impact on customer and retailer demand".
He also blamed "aggressive overseas competition".
The 5p charge for bags was introduced in England in October and followed the introduction of charges in Wales, Northern Ireland and Scotland.
One worker told BBC Radio Lancashire they believed the legislation had a "slight but not a massive impact" on the business, which has been operating since 1975 and was taken over by Cheshire-based packaging firm Intelipac three years ago.
7.6 billion
Number of plastic bags issued by supermarkets in England in 2014
140
Equivalent per person
40 bags on average in every home
Â£780m expected economic benefit over 10 years because of the charge
Â£60m savings in litter clean up costs by 2025
80% expected reduction in bags
Union representative Robert Copeland, who had been with the firm since 1986, said staff were told last Wednesday that they were being made redundant and were told to leave the factory immediately.
"It's daunting as I have no interview skills. I'm 49 years old and I've got to now go into a new working environment and start again. It is scary.
"I was 19 when I started andâ€¦ you were seeing the children of people you have been working with for 30 years starting to come through so you had parents and children [at the factory]."
Campaigners argue that plastic bags blight streets, spoil the countryside and damage wildlife, seas and coastline.
Wales was the first UK nation to introduce the bag charges, followed by Northern Ireland and then Scotland.
A report in 2015 found the number of single-use carrier bags handed out by shops in Wales fell by 71% since charges were introduced in 2011.
Scotland and Northern Ireland introduced their charges in 2014 and 2013 respectively and also saw significant drops in usage.
The number of plastic bags handed out in Scottish stores was slashed by 80% - the equivalent of 650 million carriers - in the first year of the 5p charge.
Similarly, in Northern Ireland in 2014 there was a 42.6% annual reduction following a previous drop of 71%, after charges were introduced.
Does the charge include all carrier bags?
The introduction of a 5p charge for plastic bags in England has been blamed for a packaging firm going into administration.