Is NTU short for Nottingham Trent University? To be blunt, I doubt that an LLB from there would make you a competitive candidate for jobs in US/international law firms. Even when those firms recruit university-blind, they still quite often hire candidates from the best known UK universities. This is possibly because those candidates do better at interview. The Oxbridge tutorial/supervision systems of teaching tend to be good foundations for those who wish to practise in dispute resolution, and candidates from UCL, LSE, KCL etc aren't far behind in the intense competition for places in leading firms and sets of chambers.
I don't wish to dampen your enthusiasm, but it will probably be a long hard road for you to obtain a job in the type of firm which you have in mind. It's not impossible, but you may have to think and act strategically over several years to work your way up to that level of legal practice. The upper end of the legal sector is one where the effort put into the first degree may bring rewards, and a bad or mediocre first degree can result in significant disadvantage. That's how it is.