ΔE 17.8, loose: different enough that you should pick on purpose. Battle Dress Green is a little darker, more saturated, warmer than British Camo Green.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 18). Battle Dress Green is a little darker, more saturated, warmer than British Camo Green.
The same difference applies the other way round: British Camo Green is a little lighter, more muted, cooler.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See British Camo Green on the colour wheel See Battle Dress Green on the colour wheel
All matches: British Camo Green equivalents · Battle Dress Green equivalents