Facebook has removed pages offering weapons for sale.
Revolvers, rifles and sub-machine guns built or designed in Britain were listed for sale in secret arms-trading groups on the website, according to The Times.
The weapons were advertised alongside anti-tank weapons, rocket launchers, heavy machine guns, portable anti-aircraft systems and grenade launchers manufactured in Europe, Russia and the United States, the newspaper said.
In an article on Wednesday, The New York Times referred to Facebook's "sprawling online arms bazaars".
The newspaper said it had provided Facebook with seven examples of suspicious groups, and the company had shut down six of them.
Asked if pages offering British weapons for sale had been removed, a spokeswoman for Facebook said on Friday: "Everything that has been brought to our attention and that violates our standards has been removed as soon as we saw the report earlier this week."
The Times said photographs and descriptions of the weapons, which it says were posted on Facebook and other social media platforms in Libya, were discovered by weapons intelligence consultancy Armament Research Services (Ares).
Sellers are said to have negotiated deals with buyers through private messaging and telephone conversations.
In a statement, Facebook said: "It's against Facebook's Community Standards to coordinate private sales of firearms, and we remove any such content as soon as we become aware of it.
"We encourage people to use the reporting links found across our site so that our team of experts can review content swiftly."