Cool find.
The ‘BO’ at the top stands for “Board of Ordnance” and the Board used the ‘broad arrow’ mark as an indication that an item was government property. The shield with three field pieces and three cannonballs above had been used as their armorial since the 17th Century but not given royal approval until 1806.
The Board had been responsible since Tudor times for supplying the British Army and Navy with gunpowder, munitions and fighting equipment including, ultimately, uniforms when they became standardised. Other items were supplied by various agencies including private contractors.
It is a ‘cloth seal’ and, as far as I know, wasn’t used for consignments of military equipment as such. It would have been applied to things like bolts of cloth and other textiles purchased for uniform-making and bales of finished uniform garments, in addition to any seals already applied, to protect the items as Crown property.
in 1806, the Board directed its storekeepers and others to mark "all descriptions of Ordnance Stores ... with the broad arrow as soon as they shall have been received as fit for His Majesty's Service". From 1822 the Board was given additional responsibility for sourcing, storing and supplying a variety of additional items for the Army, including tents, and other camp equipment including blankets, plus 'barrack stores'. From 1832 their remit was further expanded to food (including forage for cavalry regiments), coal and candles for all homeland troops. It ceased to exist as such under that name in 1855 after criticism of its performance during the Crimean War.
The markings will most probably relate to quantities and nature of the goods to which the seal was applied. Yours seems to have some numbers including ¾. Here’s the back side of another example (from after the Board was dissolved) and note that numbers and letters with curvature were habitually gouged in straight lines (53 here) simply because they were easier to scratch than curves.
