It was evidently immediately after Manassas that the CSA commenced seeking European ordinance stores, weapons, accoutrements, etc...
General Beauregard, post-war, lamented that the Confederate government did not contract for or purchase large quantities of British equipment in the period February-April, 1861. Only attempting to do so after the blockade was commenced.
Large shipments of arms and Accoutrements from Britain reached the South in the early Spring of 1862, with several thousand of these arms forwarded to the western armies in time for the Battle of Shiloh, etc.
By May, 1862, Confederate Agent in Britain Huse, noted the firm of S. Isaacs, Campbell, and Co., were ready to run war material through the blockade for direct sale to the Confederate government...
Illustration of a Confederate soldier at Drewry's Bluff, from the Richmond Southern Illustrated News, Sept., 1862, with British accoutrements, including snake-clasp waist belt, expense or ball pouch, and Enfield cartridge box. Evidently armed with Enfield rifle with saber bayonet. Possibly a CS Marine (?)... they were posted at Drewry's bluff, and were equipped with British accoutrements...
Here's a similarly equipped Johnny, with the percussion cap pouch, generally worn by the British on the Cartridge box belt, worn on the waist belt, American fashion...
These equipments, as shown above, were similar to those employed by the British Rifle Volunteers, like this Hampshire Volunteer Rifleman, ca. 1860:
C.L. Webster's 2009 book "Entrepot" gives a great deal more information on the specifics of the importations.
As far as their issue among the units in Lee's Army of Northern Virginia, I am not aware of any specific references, however, a few British cartridge boxes, belts, etc. with a historical provenance to Lee's army are known. For example, a British cartridge box, with outer flap removed, recovered from the Gettysburg battlefield...
Here's some original CSA accoutrement belts...
CSA belts, Jim Mayo...