A few more comments having watched the film again.
The Sea Vixen indeed has barely enough momentum to get clear of the end of the deck so it's entirely possible that it had throttle problems as opposed to a dud cat. shot.
The Buccaneer has all control surfaces apparently set as described by Beagle and it gets a good shot but it then pitches up at once almost to the vertical and climbs a little before gravity overtakes it less than half a mile from the ship.
I'm sure the Russian was the STOVL Yak-38 but so far I can only find references to single seaters. It definitely has 2 POB and makes an apparently unassisted takeoff from a standing start using most of the length of the carrier's deck. At all times its tail is down and the nosewheel off the deck. It goes straight off the end (no ski-jump) without making any attempt to fly and two chutes result.
I understand the forward opening structure behind the cockpit is not an airbrake but an air intake for the (two) separate lift engines it utilises and it would appear that perhaps these or its single main engine failed it on this occasion.
On the topic of Martin-Baker not getting a fair crack of the whip I can accept that this wasn't meant to be a film about M-B but all the producers had to do to keep the record straight was to tell how many lives have been saved by M-B seats and how many by others. QED.