Hi OP. As others have said, LSE is more if a postgrad institution. At undergrad, 70% of intake is from overseas.
My DD applied for Geography (supposedly not one if their more competitive subjects). She applied with four A stars predicted (subjects were Geography, Economics, Politics, Maths) and an A star EPQ (already achieved in Year 12). She applied to -
Oxford (rejected)
UCL - offer in Nov
Bath - offer within about 3 days
Durham - offer in about Jan / Feb
LSE - radio silence..,, radio silence until the deadline day in May... ???... still radio silence,,, she had to call them..,, "sorry you are rejected."
Bearing in mind, she applied in late Sept, how could it have taken them 8 MONTHS to respond? And even then, she had to call them - past the deadline day!
In the end, she was so worn out with the whole thing, she took a gap year, through sheer exhaustion. Second time around she applied with 4 A stars in hand, plus the EPQ A star (also had 11 9s at GCSE). She applied to -
Bristol - unconditional offer within days
Oxford - unconditional offer (accepted that)
UCL - unconditional offer in Dec
Durham - had not heard by the time she accepted Oxford in the Jan
LSE again - just for fun! Had not heard by the time she accepted Oxford in Jan - so who knows? Wouldn't have surprised me at all if they'd rejected her again in May.
Anyway, LSE did her a favour actually, because if she'd been accepted in Year 13, she probably would have gone, even though we live in London and she didn't really want a London uni, experience-wise. She had a blast at Oxford, loved the whole thing, and got a first. More recently, LSE did offer two Masters programmes to her - but she turned them down.