Just remember that LSE/KCL/UCL are ludicrously competitive for Law. They get thousands (yes, thousands) of applications each year, and many applicants who meet, and even exceed, the entry requirements will not get an offer. You could end up with no offers, or just an offer you later realise that you are unlikely to meet.
I'd suggest that you have two out-of-London choices that are not as competitive, and where you may be more likely to get an offer, and who might be more forgiving if you miss your grades next August. One tactic would be to apply to just LSE/KCL/UCL now, and leave two choices blank. Depending on any offers or rejections, you would then still have the option of adding two more strategic choices before the Jan deadline.