Other than those two things you mentioned? Nothing really, to be honest. As a UK law grad (with zero connections to India, other than the fact that my parents are from there and that we speak Bengali at home) that wants to go into academia, I can confirm that unless you want to (i) get into academia; (ii) become a barrister; or (iii) have fun (in a moderate to highly stressful academic way) for a gap year you have available to you, an LLM at any British uni, at least, not just Oxford, gives you hash other than some minor bragging rights. So right. No logic behind the mad rush.

Since you brought this up, I'm curious - what exactly does the BCL offer to Indian law graduates? For the extremely academic minded, it makes sense - to move into teaching at leading law universities around the world. The same narrow pool competes for pupillages to be barristers in the UK. On the other hand, there is no real pipeline from the BCL into city law firms. Some nepobabies are using the BCL as a cosmetic CV booster before returning to India to join the family practice.

But I do not see the logic behind the mad rush.

They look for any circumstances beyond your control. Some possible examples could include:

1. Long-term illness.

2. Long-term impact of a medical condition or disability (e.g., your law school didn't give you reasonable adjustments to support with your learning, if you are a disabled person (like extra time/computer usage in exams), or if whatever adjustments they gave didn't facilitate your best performance).

3. Similar to point no. 2 above, some other circumstance out of your control relating to disability adjustments (assuming you are a disabled applicant). Let us suppose you are blind and given a copy of the Bare Act in an exam that isn't accessible to you/isn't in the right format for you, or suppose you had a scribe whom you'd practiced with previously but that scribe fell ill... things like that.

4. Impacts of geopolitical circumstances on your studies (natural disaster, maybe even pandemic lockdowns?) that were worse for you than for others.

NB: There is a presumption that extenuating circumstances were taken into account by your law school professors when evaluating your work. You'll have to try and rebut that presumption.

NB II: You should know that a number of the Russell Group universities in Britain have much harsher policies towards exam resits (when you fail the assessment/exam of a course and give it again) than their Indian counterparts. Whereas in many Indian universities (including the NLUs) they still allow you to achieve (in most cases) the highest grade in a repeat exam, while indicating on your transcript that you had given a resit exam, these British universities do things differently. If you fail an exam without extenuating circumstances, they make you resit it, but they don't allow you to achieve anything higher than the minimum passing mark. They call it 'capping' your result at the minimum pass grade. So if you think you can repeat an exam in which you did badly without extenuating circumstances and apply for graduate study in these places, you may want to think again, because when they see those repeat markers, they are likely to turn up their noses in such cases, thinking that those students had an easier time of it than their counterparts at UK universities (whether this is justifiable or not is altogether another question, I am just stating the realities here).

anyone who is peddling the story about being in top 5 is mistaken

the academic requirement is min 65%+ for NLUs and being at least in the top 20% of the batch

your referees will be asked to select from a drop down list as to where they will put you intellectually etc. even if they put you in top 5% if your scores are not within top 20% gradewise then there is a disconnect and oxford will not take the application forward

the other way is to get reco from someone very influential either politically or a famous oxford alum etc. you have to spin a story that you are assistant of this person etc., your social work is the mitigating factor for your poor grade etc. and you want to change the world. My suggestion is to either get to union cabinet minister or a chief minister and get a reco.

Impossible. The one and only example I know of of someone who got in with less than the very best of grades is a person who read for the BA in Jurisprudence itself (Oxford's undergraduate law degree) and achieved what they call in Britain a 'high 2:1' (above 65% average overall). And that too was back in 2018, which is ancient history today. If you haven't done well until now, as far as BCL goes, just give up. Even work ex won't help you cut it, Oxford is focussed centrally on grades, everything else is icing on the cake. So where other unis will compromise to a limited extent on grades if you have five years work ex, Oxford will only take you if your five year work ex is icing on the cake whose main ingredient is top grades.

As far as I know the basic and principal requisite condition for an Oxford BCL is having good grades and by good grades, I mean be in the top 5 of your batch. Everything else on your CV will be an add on. For an LLM from a good foreign University, a diversified good CV with an okayish grade is enough, but for an Oxford BCL, great grades are essential.