I think as an external degree holder, you need to be realistic about your prospects in order to avoid disappointment, where disappointment = expectations minus reality.
Just laying out all the cards for you here. You need to have an upfront conversation with yourself.
Firstly, you don't come from the conveyor belt of local law
SMU and
NUS students, or the higher ranked or more prestigious Brit unis. That already puts you way back in terms of hiring prospects.
Its not easy to get into Big 4 law at all. People with stellar grades struggle to land a spot. This is not like other industries say accounting where their Big 4 hires an army of accounting grads with more or less average grades every year.
Landing a Big 4 training contract is perhaps like competing as a biz grad for a Management Associate position in one of the big local banks, i.e. definitely doable but not easy.
Secondly, everyone puts in the hours. The UCL law grad competing with you is probably also prepared to put in a 15 hour a day, 80 hour workweek. Hard work is not all there is in the working world. In fact working hard is probably the most straightforward thing to do, but there are so many other factors involved.
As for accepting a lower pay? Professional services firms pay standard rates according to each yearly intake. If they give you a shot, they'll pay you equally with all your peers. Otherwise, they won't even hire you at all.
Third, you cannot get called to the Bar with an external degree. Malaysia might give you a shot, but there are considerations of moving up north for a few years which you must think through for yourself. It's a long winding road if you take this path.
So you really do need to temper your expectations here. Not looking down on your qualifications or anything but this is the reality of your position.
I think before you start aspiring to the position your cousin (glamorous jet-setting in-house counsel at oil and gas etc etc), be mindful that she probably graduated from a recognised university and slogged it out at a top tier firm for a few years before ending up where she is now.
Its not impossible to become a lawyer and equalize yourself with the other law grads, but just be aware that by virtue of you taking a private law degree, there are all these systemic hurdles to cross before you can actually have a shot at progression in the legal profession. Your path will be necessarily different from the others, and definitely more arduous. But i won't dare to say that it is impossible. Good luck