I have a UCL economics offer with gcse grades 9999888877, based on the grades youve given your GCSEs look fine. Dw about one subject that is a 5, as long as maths/ english is 7 and above then its all good. So you'd defo be fine for UCL and KCL, but ive heard that LSE for certain subjects (like economics) is relatively strict on gcses.
Id also probs say to not do 4 a levels, unless the fourth one is further maths. I go to one of the best schools in the UK for a level performance, and even here Id say that most took 4 alevels but then like 50% dropped the fourth subject after year 12. That being said if its further maths or youre really smart then go for it, and if doesnt work out then drop it.