A request under the freedom of information act revealed the scale of public anger towards shops inflating prices of core lines.
The regulator said it could not reveal how many were related to convenience stores as it was still processing the data.
However, in accounts by local trading standards officers, food bought from independent stores accounted for more than half of all complaints.
Many complaints listed were towards food wholesalers. In several incidents checked by betterRetailing, online vigilante groups ‘named and shamed’ independent stores for passing on wholesaler price rises.
One retailer said: “You do whatever you can to get hold of supplies, and this is the response.”
Referencing allegations of unfair terms from wholesalers and suppliers, the NFRN wrote to the CMA to discuss “legitimate complaints regarding pricing and availability during the coronavirus outbreak”.
Trading standards departments are also understood to be carrying out inspections related to concerns around social distancing in independent stores.
A source confirmed that three post offices in Scotland were visited last week following complaints from the public to trading standards in Scotland.
Find out more on our coronavirus information hub for retailers