Weighing University Options for CS

Hi all, I am an international student currently in the UK. I have an offer to study Computer Science (BSc) at the University of Warwick. However, the tuition fees are quite high. As an alternative, I am considering pursuing a Computer Science BSc at a lower-ranked university, such as Nottingham Trent University, where the fees are about half of Warwick's. After that, I could apply for a master's degree at a Russell Group university, or possibly even Warwick.

Which option would be better for my career and long-term prospects? Would paying the higher tuition fees for a 3-year bachelor's at Warwick be worth it, or would the second option be a smarter financial decision?

I would greatly appreciate any advice. Thank you!