The Government factories had their own proof facilities on site, as did BSA and Sterling although quite what you are 'proofing' in a blow-back SMG with no positive locking is a matter of conjecture. The first Enfield made SA80's were MoD proofed on site but from Nottingham manufacture onwards they were commercially proofed at the MoD site. Bren barrels made at CRD in Cornwall were MoD proofed at a facility built at the site

There is no MoD proof for small arms now. They all go through the commercial proof house