What ways do I have of doing this? Learning a language? Improving my skills as a computer science graduate, as engineering is a specialty occupation that is in high demand in the US. What else could I do to increase my chances of a firm sponsoring me?
Engineering/compsci is indeed a specialty occupation, but the problem promptly arises that you want to work in a law firm. An engineering/tech company will only sponsor you for a visa to work for them. To be clear - H1B visas (and most other work visas) are not the sort of thing that you just get to do whatever you want in the USA once you have the visa. A specific company or university sponsors you. While you are in the USA you can only work at that company. If you quit that company you cannot remain in the USA.
It brings us immediately back to the original point - how to you persuade a US law firm to take you. As stated, the only way to go into a US firm's office "from the ground level" is to have a JD. As stated, the best way to improve your chances of doing that is to go to a top 15 law school. That is how you better your chances. That and good university grades.
Do I even have the chance to apply to any of these law schools with my GCSEs & A levels? Would my application be competitive?
Are your grades good enough for a top 15 law school? I don't know. I don't work in admissions. I'll be honest - they certainly won't help you, and you will certainly struggle, but as you have probably picked up, you will have an uphill struggle getting into corporate law anywhere.
This is also very much a case of putting the cart before the horse. You can't go to law school until you have done undergrad. So don't worry about US law school until you are actually at that stage. For now work on your university grades. Those are extremely important. Have a google and you'll see that good law schools have a high average GPA acceptance standard. If along the way you decide that you're willing to work in a firm in the UK, then those great grades at university you've worked so hard to achieve will stand you in good stead, and can - to an extent - help balance out your poor A level grades.
Moreover, how would I finance this if I was (by a miracle) accepted into one of them?
Financing is of course another question. Some people are lucky enough to get scholarships: others take out a loan. In the highly unlikely event that you were to get an offer from Harvard Law, the debt you'd have at the end would be wiped out extremely quickly, because US firms pay a lot for Harvard law grads.
Is it unlikely? Oh yes, of course. I'm not going to lie to you, it's highly unlikely - for anyone! It's a very competitive and lengthy process. However, it's the only way of working in America from the very start of your career, which you seem set on doing. It is not a particularly feasible option, and is complicated and tricky at the best of times.
Personally, I would concentrate on your undergrad modules for now. Go to law fairs, do research, and so on. Second year, apply for vac schemes (potentially third year too). You can apply to US firms (albeit their London branches), see what happens. Work as hard as you can at your undergrad degree. See what happens. Ideally, by the end of your undergrad degree, you'll have a much better idea of where you stand, how interested firms are in you, how good your grades are in relation to US law school.
