Blake's 7/WMG

Only Blake and that other woman died on Gauda Prime.
Fans debated the Bolivian Army Ending of the series for almost three decades. Argument: Blake went squibby; the others just fell over.
 * Fighting in Blake's Seven was often abysmally choreographed. Or, to put it nicely, fighting in B7 was very much symbolic.
 * Gareth Thomas has confirmed on numerous occasions that his primary stipulation for playing Blake one last time was that the character be seen to die, with absolutely no ambiguity over his fate. That's why blood squibs were used, to underline that Avon's weapon wasn't set to stun. Chris Boucher, the writer of the episode, and Paul Darrow (Avon), have further confirmed that the fates of the other characters were kept deliberately ambiguous to provide flexibility had a fifth series gone into production, which at that time was still a faint possibility. The actors who wanted to come back would have been stunned, the actors who didn't would have been killed. Well, not the actual actors, but their characters. YKWIM.

The whole Bolivian Army Ending is an illusion or mind game, like 'Terminal'.
All of a sudden, Soolin is from Gauda Prime? Dead giveaway.

The gunfight on Gauda Prime was the culmination of a Xanatos Gambit by Servalan to get her hands on Avon and Orac
Here's the Gambit, in summary: Servalan would love nothing more than to teach the Federation a lesson for ditching her as President. She's been trying to do it from the inside as Sleer, but her freedom of action has been restricted. She needs an external threat to give her that freedom. Avon is the perfect external threat, and one that she can easily manipulate. Getting Orac is necessary for obvious reasons, especially those dealing with protecting her Sleer cover. But to do this, Avon has to be removed from any support system he might have. She has to get rid of Scorpio, its crew, and Blake. She finds out where Blake is, confirms it, and then sets things in motion through her agents on Gauda Prime to bring everyone together to eliminate everyone in one shot. The shots fired after the blackout were Servalan's "cavalry charge" killing the men surrounding Avon, just to make sure that Avon was in her debt. Orac is removed from its hiding place - and off they go.

The only thing she may not have counted on - and knowing her, she has - is how mentally unstable Avon is. If she planned on Avon being the one to kill Blake, this veers the whole plan into Gambit Roulette or Xanatos Speed Chess territory; that's not Servalan's style.
 * Remember that Servalan has successfully pulled off Xanatos Gambits like this before and made Avon look like a Butt Monkey in the process. (See "Gold").

Star Trek and Blake's 7 are depictions of the same universe
Neither is entirely true or accurate. Star Trek is big-budget official government propaganda. Blake's 7 is produced on a shoestring by a group of angry malcontents.

This idea has been around for years.

The Federation of Starfleet deteriorated into the Federation of Blake's 7
This was part civil war, part genocide against most alien species, and part the most militant faction of the Federation (Section 31) coming out on top and ruling the roost.

Look how the upper echelons of the Federation behave in Berman's Trek: the president and people quietly accept martial law, Section 31 is continually scheming; the Federation abandons its own colonists to the Cardassians to appease them, etc. It is NOT much of a stretch. Julian Bashir, who proposed surrender to the Dominion with a straight face, was Avon's grandfather.
 * For this this work, transporters and replicators would have to become Lost Technology.

Firefly takes place in the same universe.
The last series of ''Blake's 7' introduced Pylene-50, which worked in very similar fashion to the Pax only without the side effects, and the domed cities on Earth and the restrictions on outside movement could quite easily have started out as a response to some kind of environmental catastrophe. It would be entirely typical of the Terran Federation to keep a Lost Colony too backwards and resource-poor to be worth annexing embargoed as a proving ground for their latest mood-stabilising drugs or other instruments of totalitarian unpleasantness. Whether the Alliance government is an Unwitting Pawn or willing accomplice is anyone's guess. (Cross-posted from the Firefly WMG page.)

The Doctor's actions in the Waters of Mars caused the existence of Blake's Seven's timeline
Expanded universe material for Doctor Who has suggested that it takes place in the same universe as Doctor Who, such as the appearance of a minor guest character in the novel Corpse Marker, written by Chris Boucher himself. However this contradicts some of the show's lore as the The Ark in Space shows that humanity has already discovered teleportation despite the Liberator being the first example of it in the Blake's Seven universe which would seem to contradict Who. However, as Steven Moffat would say time can be rewritten. One huge difference that the Doctor did cause in the Waters of Mars is that now there are two survivors humanity knows that it was alien life forms that were responsible for the destruction of the Mars base. This will likely lead to a much more cautious and likely hostile reaction to any future forms of alien life they may encounter.

In the original timeline Adelie Brook's granddaughter married into an alien dynasty, but growing up with the knowledge that the Water Creatures caused her grandmother's death will leave her much more close minded, and will likely make her campaign to explore space a war of aggression rather than discovery. As a consequence of this aliens will be pushed back and shunned by human advancement, leading to their scarcity and recourses that were originally funnelled into civilian projects like the teleporter will instead be used for the advancement of the military. The reactionary, paranoid climate brought about by the disaster will provide the perfect conditions for the militaristic, fascist federation to begin.

The Blake's 7 universe is the 51st century of Doctor Who

 * While Jack and River are out being liberal and omnisexual in the outer colonies, Earth itself degenerates into an insular fascist state that treats human-descended residents of distant planets as aliens. Magnus Greel is last ruler of the Federation before it collapses and gets replaced by a better government.

Travis's Sanity Slippage was deliberately caused by Servalan.

 * She had the Federation's Psycho Psychologists do some nasty things to him between the two seasons to make him more dangerous to Blake, less likely to turn against her, and less likely to attract sympathisers if he did.