Here are the measurements of the 400/360 WR rimless cartridge.
Reference . British sporting rifle cartridges by Bill Fleming ( if you can find this book. buy it.)
Case length 2.740"/2.748
Rim Dia .465"/.468"
rim thickness .049"/.059"
Base .465"
Shoulder .415"/.420
Case Mouth .382"/.385"
Bullet dia .359"/.360"
O/A Length 3.585"/3.592
Kynoch loaded 4 bullet types
all loads had 41 grains of cordite and a 314 grain bullet
Round nose cupo nickel solid
" ' " ' soft nose
" " " soft nose split
Westley Richards round nose capped
all bullets were non magnetic.

Apart from the usual red and yellow box there was also white/yellow label white/white label and brown.
The case was head stamped kynoch 400/360
Where the rimmed case has as many as 24 different head stamps.

Hope this helps