GPA and extracurriculars (depends on what extracurricular) absolutely do matter to uk universities. There may not be a requirement for a minimum GPA or extracurriculars you have to have done, but they will look at your grades and your extracurriculars to see if you are a well-rounded person
For LSE:
LSE is the most prestigious and selective school in the UK and the second best school for social sciences in the world and out-ranks all the other schools you have listed. I highly recommend viewing this school as your first choice.
Be aware that this is an extremely academically oriented school. They do not conduct interviews and the only way they get to know you personally is from a 4,000 character personal statement. This means you academic qualifications are key. They do not look at SAT scores or any other standardized test. LSE looks for extra-cirriculars that relate to your intended degree. For example, I also want to attend LSE and obtain a degree in government and economics and have been working to that since freshman year. So one of the clubs I joined was the Model UN team and have done only economic based committees and have won awards. This shows my interest and experience in both world government and world economic matters. I have also done peer leadership at my school, but that will mean little to LSE other than my leadership skills because it has nothing to do with government or economics.
LSE’s main entry requirement for students to even be considered for lower level degree programs must have taken 4 A level ap courses and have gotten a 5 on all the tests. For a most programs and all math based programs you need to have taken at least 5 A level ap courses and have gotten a 5 on all the tests. If you do not meet these requirements, DO NOT EVEN BOTHER APPLYING. You have taken a lot of math-based ap tests so I assume you want to obtain a degree in a math based field (economics, finance, accounting etc) which require 5 a level ap courses. (to see which ap courses are considered A level and which are B level view this link https://www.ucas.com/ucas/undergraduate/getting-started/entry-requirements/tariff/tariff-tables/966). From the ap courses I see above you only have 4 A level ap courses. Ap calculus BC, AP European History, Macro and Micro economics (2 B levels count as one A level), and US and Comparative Government and Politics (2 B levels counted as one A level). Psychology and Statistics are considered as not suitable for entry at LSE and Physics will only count as an A level if you have taken both the B and C tests. That being said if you apply to LSE for a program that requires 5 A level AP courses they will not even consider you. I strongly suggest you take at least another ap this year. They will allow you to apply even if you have not taken all your tests but you will be required to submit your grades you currently have in the course and their admissions tutor will predict your ap test grade. Depending on whether or not they predict you will get a five that will count as 1 A level ap course. Because you have to submit grades in an ap course for prediction of the test outcome do not self-study it on your own as there will be no way to predict your test grade. Taking it through school is best, but if you simply don’t have time in your schedule take it through an accredited online cite such as John Hopkins Center for Talented Youth.
I strongly suggest taking an ap english course as applicants who don’t have english as their first language will be required to take a test to see if their english skills are proficient. Not only will taking an ap english course wave the requirement of the test, but it will also set you apart from other applicants in your geographical area. AP language and Composition is especially helpful for writing.
Be aware that most applicants applying based on ap tests have exceeded the minimum requirement. When I apply to LSE I plan to offer 9 A level AP courses with another one in progress. That being said I strongly recommend you take as many A level AP courses that LSE considers as suitable for entry as possible. While taking more AP history courses will look the best to LSE, taking any AP A Level that LSE looks for will improve your application
To view which A Level AP courses are considered as suitable for entry at LSE view this link. While this is the USA requirements page the AP requirements are the same for all countries. 2 AP courses listed together are 2 B levels that when taken together, will count as one A level.
http://www.lse.ac.uk/study/informationForInternationalStudents/countryRegion/northAmerica/USA/entryRequirements.aspx
Not only have most people exceeded the minimum requirements but most applicants have also. So writing a stellar personal statement is key. In this you should show your enthusiasm for the degree you are applying for. You should tell what books you have read, internships you have done, lectures you’ve attended, and what extracurriculars you’ve done to show your initiative in that area. Because academic qualifications are so high in the applicants at LSE, writing a superb personal statement is what gets people accepted there.
For Oxford
A little less complicated for Oxford. You currently exceed the SAT and AP minimum requirements for Oxford. Just make sure that when writing the essays and attending the interviews you show your enthusiasm for the degree and what you have done outside of academics.
For UCL
You currently exceed the SAT requirements. You meet the requirements for the AP scores if the AP tests were taken in the final two years of your high school. In addition you must have completed one year of study at a university with a minimum GPA of 3.3 out of 4. An international foundations program including a UCL undergraduate preparatory certificate can wave this requirement. Once again if you have completed these qualifications you will have exceeded the academic requirements. All you have to do is stand out in Essays and in Interviews.
For Imperial College
They looks for just 3 AP courses with a five in all of them, which you exceed. Just make sure, again, you stand out in essay’s and interviews.
You should consider King’s College and Cambridge as they are both very prestigious and selective and are very similar to the other colleges you mentioned.