Firing a Bren in fully automatic mode, it vibrates a good deal, but doesn’t kick the way a high-velocity rifle kicks. If anything, it pulls forwards. I think this is a consequence of the design of the gun.

When a Bren gun is fired, the gas propels the bullet along the barrel, up to the gas regulator, at which point a portion of the gas is applied to a piston that drives the working parts backwards. The working parts are being driven back against a spring that, when the forces balance, brings the working parts to a halt and then, when the (diminishing) gas pressure exerts less force than the spring, drives the working parts forwards to load the next round into the chamber. As the working parts slide forwards, there is no spring that brings them to a gradual halt. Instead, they slam against their end-stop (which exerts a large force for a short period of time, on account of f = ma) and the firing pin (assuming the trigger is held down) is the only part that is free to move forward any further.

Since the weight of the working parts is considerably larger than the mass of the bullet and the propelleant gases combined, I think the biggest change of momentum involved is that engendered by the working parts hitting their end-stop at the end of their forward motion.

I think that considering the problem from the point of view of ideal collisions and momentum conservation is not the right approach – instead, it should be considered from the point of view of forces and accelerations.

From this perspective, the relative masses become extremely significant, as does the drag of the water.

If we arbitrarily say the force applied by the gas pressure in the barrel is 10 N, and the mass of the bullet is 0.01 kg, and the bullet is accelerated for 0.1 s, then it gains a velocity of 100 m/s at an acceleration of 1000 m/s².

If the mass of the boat etc. is 100 kg, and we assume no friction, it is accelerated at 0.1 m/s² for the same time to end up moving at 0.01 m/s in the opposite direction. Given friction from the water, I cannot imagine how you would ever notice this imparted velocity.

Now, of course my figures are chosen for convenience and only approximate the reality. However, if I’m right to within an order of magnitude (are there any machine guns that generate a muzzle velocity of 1 km/s?), you would never notice the momentum imparted from firing one bullet above the vibration of the gun. From 100 rounds, and still assuming no friction, you might impart 1 m/s to the boat, but in reality we do have friction.

The boat is accelerated backwards at 0.1 m/s², applying 10 N to the water. I have no idea how much friction water can apply to a boat, but a frictional drag of 10 N does not sound outlandish.

^_^J.

would thermal expansion of the metal cause the bore to narrow?

Given the fact that heating a too-tight lid on a jar can loosen it by expanding the metal, I would have to say “no”.

Then again, to maintain the acceleration, he would need to keep up continuous fire of the MG, and after perhaps 1000 rounds the barrel would start to distort as it heats up (would thermal expansion of the metal cause the bore to narrow?).

I know that the SA80 in the sustained fire role has a cooling jacket on the barrel, and LMGs such as the Bren from WWII would normally be carried with a spare barrel, which needed to be changed after about 500 – 600 rounds of prolonged fire.