got a 4 in maths GCSE and a 9 in english. Is it worth applying to LSE or UCL?

I'm predicted A*AA for A Levels (Econ, Politics and History) but both LSE and UCL have requirements for GCSE maths and english to be above 5 or 6, due to personal reasons (and I have evidence to support if necessary) I struggled with attending in Y10 & 11 which severely affected my final results. Entry requirements for my course is AAA, but I'm predicted higher. Should I apply despite my lacklustre GCSE grade?

Universities are normally pretty firm (non-flexible) on their GCSE requirements, and I would not expect LSE or UCL to be any different. They would likely argue that since the issues you encountered in Y10 and Y11, you've had a full year to retake GCSE Maths. In fact, by the time the A level results roll around, you'll have had two years.

My advice would be to register to retake GCSE Maths as a "private candidate" somewhere (or as a "regular" candidate at your current sixth form / college if you can), and then drop it on your UCAS form with a "Pending" grade. If they do make an offer, they'd include obtaining grade 5 (or 6) in GCSE Maths as one of the offer conditions.