Law @ KCL/Bristol/Warwick - Is there much of a difference in career prospects?

I'm an international student applying to universities in the UK and can't decide between applying to both Bristol & Warwick, or swapping one of those out for KCL. Since money is a big factor, I'm leaning toward Bristol and Warwick as they are cheaper than KCL.

However, KCL is ranked slightly higher, and I wonder if choosing Bristol or Warwick might hurt my chances of getting a job later. I'm aware that all three universities are great for law, but as an international student, getting a job in the UK might already be harder. Would KCL give me a significant advantage over Bristol/Warwick for pursuing a career in Magic Circle/Silver Circle/US law firms, and is that advantage large enough to warrant the hefty price of KCL's course?

Thank you in advance for any advice :)