One of the rifles I just brought back from the mainland.  Research convinces me that this is a #5 MK I, not a cut-down No.4 as is so often seen.  It has a couple of peculiarities, including an almost total lack of markings.

Photos here.

Odds are it's a BSA.  They were known for light markings, and it does bear a proof stamp from their Birmingham factory.  But aside from that proof, the receiver is devoid of markings. 

Can't wait to see the reception I get at HPD for a gun that has no manufacturer, no caliber, and no serial number!

can't help ya out, nice carbine

Here's a picture of an original refurbished RFI jungle carbine. Also if I remember correctly there is a difference between the regular rifle rear sight and the jungle carbine. Some thing about sight distance markings not going out as far as the regular rifle not sure though. I was researching this years ago when security equip. Had one on there rack.

This is what I found on wiki

The easiest way to identify a "Jungle Carbine" rifle is to look for the markings on the left hand side of the receiver; a genuine No. 5 will have "Rifle No 5 Mk I" electrostencilled there,[15] while a post-war conversion will generally have either no markings or markings from manufacturers who did not make the No. 5 Mk I (for example, Savage or Long Branch).[2] Santa Fe "Jungle Carbine" rifles are so marked on the barrel.[14]