Should I Re-do an LLB at a Different University?

What is the end goal here?

Getting a higher classification and a UK law degree (I currently do not study in the UK), so that I can pursue law in the UK.

Realistically UK law firms are likely to consider your original degree result anyway - doing a second undergraduate degree isn't likely to ameliorate that. Obviously if you need to qualify in law in the UK, you may need or want to do a conversion course (such as a graduate diploma in law/GDL course). But a second undergraduate degree won't erase the first one, especially if it's in the same subject area.

Your best bet would probably be aiming for getting a foot in the door as a paralegal and developing a good deal of work experience, then aiming for less competitive firms (regional offices and such) for a training contract. A strong performance in an LLM might help ameliorate a weaker undergrad a bit maybe too? Although for becoming a solicitor it's probably really overkill and with a 2:2 for your original undergraduate degree the barrister route is probably unlikely.

Could also look at solicitor degree apprenticeships, although I think these are usually not aimed at graduates or at least those with a law degree already (but if your degree is from another country, they may consider you).

From what I've seen, LLMs don't compensate for weak performance in an undergraduate degree. I often find myself saying I wish I could start over with an LLB just because I was so lost at Uni in my first year, and my poor performance wasn't due to extenuating circumstances, but was due to not knowing how to effectively study and how to cope with my studies with ADHD. Now that I'm medicated, my grades are so much better. But due to each year being weighted equally in my degree, my average is significantly pulled down. I can't really defend myself with Uni's because it doesn't really constitute an 'extenuating circumstance'.

ADHD is a valid extenuating circumstance if it wasn't properly identified or supported before, at least within universities. Employers may be less interested in that in terms of explaining degree performance.

Ultimately I think if you've gotten your degree already you just need to accept it is what it is and move ahead with things. Get work experience and start from the ground up, paralegaling until you have enough experience to be a competitive applicant for training contracts by virtue of actually knowing and doing the job already for some time.