Want to sue the university

The part where you started to get snippy and accuse me of attacks for telling you not to waste your money, not 1 person here inc several education professionals, thinks such a lawyers letter/approach would work. That's not being dismissive, it's the reality, we know that letter will do 0 and cost £200+.

How do I know if they have simply continued to set me up to fail

I don't - but you've got a chance to qualify, it seems silly to waste it by distracting yourself with grand plans to sue.

I think in that case you are falling for the sunk cost fallacy, where you have committeed a lot to an endeavour, so you must persist with it no matter the likliehood of a postive outcome.

Both myself and The_Lonely_Goatherd have alluded to the fact that legal action will take an extraordinary amount of time, money and mental energy. I appreciate there is a strong sense of not wanting them "to get away with it" or do the same to others, but you have to weigh up the likliehood of success versus what you've got left in the tank and what you could better be doing with that expenditure.

I don't think anyone so far thought that suing would be a worthwhile expenditure of your time, effort and money.

No one can tell you whether you want to do it anyway.