Bren's existing production line was cancelled historically, 1st because the Taden is to be produced, 2nd because the FN MAG is to be produced.
IIRC the Taden was a modified Bren. But since the Taden wasn't ever adopted, I think the Bren carried on in production; wikipedia says it stayed in production until 1971 and was converted to the 7.62 NATO cartridge.
The FN MAG only entered service in 1958, so was nearly a Vietnam era weapon, entering production in Britain only in 1961:
https://en.wikipedia.org/wiki/FN_MAG#British_versions
The 'belt-fed FG 42' has it's appeal, too.
It shouldn't have been too tough to pull off seeing as there was already a side feed; with the ability to say add some sort of rotary mechanism to pull the belt through it should have worked fine (see the Swedish BAR belt feed mechanism...although flawed it could work with some development effort).
Since the Taden was supposed to just be a modified Bren for the .280 cartridge and belt feeding, there shouldn't be much of an issue 'beefing up' the FG42 for the MMG role with a belt feed system. Maybe it will end up being a British M60. Though if it uses mostly the same parts and factory lines for the MMG and rifle it could end up being more cost effective than the Taden+EM-2 that was planned, especially if already using an existing production cartridge. Still, it would be hard to image that even a 'less powerful' 7.92 SME Lang cartridge would replace the desire for something like the 7.92 Kurz having encountered it in battle. It would be interesting if the Brits ended up with something like what CETME developed, the long, light 7.92 aluminum bullet to get both range and low recoil/low weight per cartridge without having to switch calibers or cartridge case production equipment.
Still all that said, a belt fed FG42 with a plastic ammo box mounted underneath the receiver like modern SAWs could make it an early PKP or HK21, but even lighter.
Edit:
Or like the KAC light assault machine gun that Gun Jesus just showed off on his YT channel.