The numbers look like part of the NATO Stock Number (NSN) which all equipment used by NATO members have.
It is a 13 digit code laid out as XXXX-XX-XXX-XXXX. The first four numbers being type of kit, second pair country identifier, next seven the actual part number. In the UK quite often just the last 7 are shown on the item of equipment itself. Sometimes there is a series of letters and numbers before the start of the actual NSN.
An example I have to hand (so to speak), my Gloves Combat MkII are NSN CM/8415-99-978-3713. The 99 signifying UK
After a very quick search along my theory i found this which is a current NSN (it does not mean the ensign you have is new though just that that NSN is still in use for RN Ensigns)
RN Ensign NSN 8345-99-571-3291
Further examples of NSN’s and description
NSN 8345-99-125-1126
FLAG,NATIONAL:UNITED KINGDOM;1220MM LG;610MM WD;CROSS MIDDLE DESIGN;FITTED WITH PLAIN & SWIVEL INGLEFIELD CLIPS;ROYAL BLUE,WHITE & RED.
NSN 8345-99-125-1117
RAF Ensign, 92X184 cm
The arrow as stated is the typical British Government Property Crowsfoot
The boxed number on many items of kit is usually the packer/checker ID number, not always though.