"Bless 'Em All" (Fuck 'em All) is listed in the Traditional Ballad Index cufresno. It is dated 1916 and credited to F. Godfrey?

Much more discussion, and several versions, are given by Ed Cray in his "Erotic Muse." Ewan MacColl noted that this song has "been the anthem of British Fighting Men since World War 1. Anthony Hopkins, 1979, "Songs From the Front and Rear," p. 105, credits the song to F. Godfrey, 1916, and linked with the Royal Naval Air Service.
The song was not copyrighted until 1940, by Hughes and Lake, as noted in posts above.

Of the several versions, Cray gives pride of place to the British Army version. The first verse is essentially the same as the WW2 British version in the DT, but with the "Fuck 'Em All" chorus.

FUCK 'EM ALL

They say there's a troopship just leaving Bombay,
Bound for old Blighty's shore,
Heavily laden with time-expired men
Bound for the land they adore.
There's many a soldier has finished his time;
There's many a twerp signin' on,
But they'll get no promotion this side of the ocean,
So cheer up, my lads, fuck 'em all.

Chorus;
Fuck 'em all, fuck 'em all,
The long and the short and the tall.
Fuck all the corporals and W. O. Ones,
'Cause we're sayin' good-by to them all,
As back to the billet we crawl.
They'll get no promotion this side of the ocean,
So cheer up, my lads, fuck 'em all.

Alternate chorus:
Fuck 'em all, fuck 'em all,
The long and the short and the tall.
Fuck all the sergeants and their bleedin' sons,
Fuck all the corp'rals and W.O. ones,
'Cause we're sayin' good-by to them all,
As back to the billet we crawl.
They'll get no promotion this side of the ocean,
So cheer up, my lads, fuck 'em all.

Cray also prints a variation on the Lancaster version of WW2 (in the DT):

They say there's a Lancaster leaving the Ruhr,
Bound for old Blighty's shores,
Heavily laden with terrified men,
Shit-scared and prone on the floor.
There's many a flak gun shooting them down,
There's many a night fighter, too,
But there'll be no promotions,
This side of the ocean,
So, cheer up my lads, fuck 'em all.

Chorus:
Fuck 'em all, fuck 'em all,
The long and the short and the tall.
Fuck all the sergeants and WO-1s,
Fuck all the corporals and their bastard sons,
For we are saying good-by to them all,
The long and the short and the tall,
There'll be no promotions this side of the ocean,
So, cheer up my lads, fuck 'em all.