Beckingham was educated at Merchant Taylors' School under Dr. Smith, and is said to have displayed "great proficiency in his studies", and given "the strongest testimonials of extraordinary abilities".
On 18 February 1718 Scipio Africanus, a historical tragedy in the regulation five acts, was produced at the theatre in Lincoln's Inn Fields.
This was followed at the same house on 7 November of the next year by a second work of a similar description, entitled Henry IV of France.
The youth of the author, and the presence of a large number of his fellow-students who had been permitted to visit the theatre, gave some éclat to the production of the earlier work.
The plot is founded on a story told by Livy and other classical writers concerning the restoration of a beautiful captive by Scipio Africanus to her betrothed, the Spanish prince Allucius.