The poll by the watchdog found 56% of consumers in England and Scotland support a 5p charge for bags but, among those opposed to a charge, 70% think they already pay enough for their shopping and 45% think they should be entitled to free bags.
A charge is already in place in Wales while Northern Ireland is introducing one next year.
The survey also revealed that half of shoppers who have used an online supermarket in the last 12 months felt too many bags were used.
Supermarkets provided nearly 800 million more single-use plastic carrier bags last year than they did two years ago, according to figures from Waste Resources Action Plan (Wrap).
The 10% increase pushes the number of bags supplied to shoppers to eight billion, or 120 per customer, just for supermarkets.
Although 8% of people surveyed by the consumer group confessed to throwing away bags in the general waste after their initial use, 92% said they do reuse bags either for shopping (53%) or as bin liners (74%).
Marks & Spencer is the only one of the seven supermarkets to charge for bags, resulting in a 78% drop in bag use at its stores.
A Defra spokesman said: "We want to work with retailers to help them lift their game to cut the number of bags they hand out. We are monitoring the results of the charging scheme in Wales and the outcome of the Scottish consultation on a charge."