Technically yes, although it would be a ton of work.
As the Bren uses an interrupted thread, as well as lacking the same extractor cut as a SMLE, you would need to cut the barrel back, cut new threads to match the SMLE receiver, as well as an extractor grove, and then recut the chamber.
After that, your only issue is the Bren barrel having a gas port, which would need to be capped in some way (pin and weld it shut, make a false gas block, etc) although the spot would still result in uneven wear in the barrel due to collected fouling.
So while it could be done, you'd burn up a bunch of time and ruin a good Bren barrel. Personally if you want a heavy barrel, I'd just buy a .303 barrel blank and cut the threads and chamber in it, which would give you something similar to the Mann accuracy device.