Hey I'm a first year lawyer at LSE - like everyone has said it's a pretty personal choice, try and attend a LSE open day (that's how i made my decision) and see what feel you get from the uni. I know that LSE give you career support for up to 5 years after you graduate, but I'm sure UCL has something similar. I run an instagram page (@in2_law) with my friend who is a first year lawyer at Cambridge - feel free to check it out, it might give you a better insight into the universities.