The ban was introduced by the previous Conservative government to cut serious violence and crime.
It widened the definition of zombie knives, which were already banned, to include knives that were 8in (20cm) long, if they had other specific features.
The Home Office opened a month-long surrender and compensation scheme before it became law on 24 September.
It offered to pay a minimum of £10 per knife to retailers and individuals handing in three or more.
But research suggests knives of the type banned could be bought far more cheaply than this.
It comes after an investigation found illegal blades were still available to buy online, a month after they were outlawed.
An impact assessment, external shows the Home Office thought owners would hand in 472 blades, resulting in compensation of about £14,000.
Officials would not reveal the actual total but said the results of the scheme would be published “shortly”.
However, partial data from several police forces in England and Wales shows at least 39,000 knives were surrendered.
One retailer in the West Midlands handed in more than 100 blades.
Nottinghamshire Police said it saw 455 knives surrendered, external, while Avon and Somerset had more than 1,000, external.
On 9 September, Luton-based Sporting Wholesale delivered 35,871 blades to Bedfordshire Police and made a claim for compensation.
There is no suggestion the firm did anything illegal or intended to profit from the scheme.
Among the knives it surrendered were hundreds of a blade known as k-mach-165.
