i think your gcses are great. but as someone has said unis like UCL/LSE are very competitive so it won't be easy getting into those.
but it may also depend on what secondary school you went to i.e. state or private. I went to a bog standard state secondary and got grades similar to you. but compared to the average in my school or even to other state schools in my area I did really well, in fact above average, so I think this was looked upon quite highly, whereas if you went to a private school, where people regularly achieve 9A*s, then our grades aren't great compared to them! I was told that unis do take into account the state or private education of applicants so they can get a good mix of students, and to meet targets. But it would be great if someone could tell me if this was true.
But either way be proud, you've done well. Good luck