My treatment being in the public sphere will be a big blow for them, simply because of what the company does. (Think care home discriminating their employees due to age or a specialist SEN school harassing their employees due to their disabilities etc.)
I don't mean to minimize what you've been though (It's clearly had a significant impact and I admire your determination to seek justice), but to be frank, unless your treatment was so egregious as to be borderline criminal, or the first domino to fall in some kind of national scandal in your industry that impacts the general public, the media will likely not care. If there's no pressure from the media/general public, the blow unlikely to be as severe as you might think.
Even if your former employers do catch a bit of flack, they'll have already prepared for the worst. They'll chuck someone under the bus, or paint the whole process as a welcome learning experience and spin it into a positive message about how progressive they've become. At worst they'll go on the attack, say they completely disagree with the outcome, that the tribunal got it wrong...and people may even agree with them.
It might be a bad luck to them, but will it stop them all from going to work the next day? If the answer is no then they'll get past it.
An anti-animal cruelty charity sacked a man for exposing that their pension funds were invested in a company that carried out animal testing, after he objected to it on the grounds of being an ethical vegan.
Your former employer won't learn a lesson by losing a tribunal - if they were that concerned about the potential reputational damage, they wouldn't have sacked you in the first place.
I understand that you feel you have a good case, but as others have said, good cases lose all the time, for a myriad of reasons. Have you considered how you'll feel if that comes to pass? If the employer is found to have acted properly on the evidence, they're vindicated privately and publicly. If you lose on a technically, or because you're unable to compete with their legal team, that'll surely feel even worse and the unfairness of it will gnaw at you for some time.
At least with a settlement you'll have something to show for the process.
I knew that in terms of insurance and how they push for settlements, however, surely they cannot pressure the claimant in any way to come to the table, so to speak?
Not directly. A good brief may indeed advise you that you have a strong case, but they will almost certainly advise you to accept a reasonable offer if one is presented. That's where the pressure is. At some point, even if it's on the day, the employer's insurance will almost always authorize a settlement comparable to what you'd likely be awarded by the tribunal.
That's the reason 85-90% of claims are resolved without a final hearing - claims that get that far are unlikely to be black and white. That's reflected by the fact that it's almost a coin toss success rate for those 10-15% of cases that are actually heard (current figures show a 42% success rate). It's unlikely to be worth the risk for either party, moral issues aside. FYI, discrimination cases have