'Not English Make' was applied by the English Proof House (either London or Birmingham) at the time of proofing of the firearm. It was used/applied to any firearm that was "not of English manufacture".
The Proof House mark was in use between 1925 and 1955.
Nothing to do with export/import.
The firearm could be of sporting use or one destined for Military use.
X-military firearms surplused by the English gov't (Sold from Service) would be proofed before allowing them to be sold and traded on the commercial market. If one of these were not an English mfg'r (P14 Enfield for example), it would receive that marking along with proofing if it was going out onto the civilian market.
The proof marks themselves will each be inside of a circle,,another demand of the English proofs applied to non-English manufactured firearms proofed during that time period.
Wether proof was done at Birmingham (the vast majority were) or the London Proof House can be determined by the small proofs themselves.
The Birmingham marks are easiest to see as they all have a 'B' in them (BNP,,BV,,ect.),,again each mark should be inside of a circle and a crown should be atop each circle mark stamping.
Those done during the hectic days of WW2 will sometimes show some lack of uniformity,,but for the most part they followed their Proof Laws straight away..