(All emphasis in the following quotes is mine)
For LSE, your chances are reduced because of the retakes. How greatly they are reduced is not completely clear, but reading between the lines I think it is a long shot.
https://www.lse.ac.uk/study-at-lse/Undergraduate/Prospective-Students/How-to-Apply/Admissions-Information"Given the competition for places and the nature of assessment at LSE,
we prefer students who have achieved high grades in their first attempt (and in one sitting) at relevant examinations. If extenuating circumstances have impacted your exam performance, you should include details of these in your application."
Imperial says similar, allbeit less stronngly worded, (unless we look at a department level FAQ which we'll come to in a moment).
https://www.imperial.ac.uk/study/help-centre/undergraduate-admissions/-what-are-the-entry-requirements-and-what-qualifications-do-you-accept.php"With the exception of our MBBS Medicine programme, candidates who have retaken exams
may still be considered for entry.
However,
submitting grades based on resits may be noted by our Admissions tutors. Where there are extenuating circumstances, these should be outlined in the reference which is supplied as part of your application by a teacher, adviser or professional who knows you academically."
However it looks like the appetite for retakes is determined at department level. Here's what the Maths department say, but you need to check with the specific academic departments running whatever course(s) you're considering.
https://www.imperial.ac.uk/mathematics/undergraduate/degree-courses-and-admissions/faqs/"You are welcome to apply, but we do have a preference for first-time A-level sitters and
usually only make offers to re-sitters if there are mitigating circumstances that meant their first set of results did not show their true potential."