[Edited by kasha21 on Jan 18, 2021]
Hi, take this as completely speculative but based on my personal research, you should be fine for KCL. I'd like to think you are fine for UCL as well as they require evidence of first-class ability which they define as just one module as a first. Seeing as you said your final year is a first, as long as you nail your application you should be fine here. I know people who got into UCL's LLM with 63s. With LSE, though it's not impossible it is unlikely because they ask for a strong 2.1 and usually receive a high volume of applicants with a first overall. However, you miss 100% of the shots you don't take, so shoot your shot. Especially if you go to a prestigious university that is known to have strict marking, they will understand. I have friends that have gone to Cambridge for the LLM programme with a 2.1 in their first and second year but a first in their final year. Though I'd like to highlight once again that this is based off my personal research. Wish you the best of luck! :)
[Edited by Omar44 on Oct 29, 2020]
Article Mar 15, 2018
Having a stellar GPA may not be the only factor that will get you into a top LL.M. program.