I would say, definitely reconsider your decision. Careers-wise LSE might be one of the best, and there's no guarantee you getting an offer elsewhere, especially with how competitive certain courses become at Oxbridge - even AAA might just not cut it. Personally I would suggest for you to perhaps consider taking more optional modules in your desired area, trying an internal switch, or continuing and doing a Master's in your desired field. You've to remember History and English Literature are different. Putting this off might give you time to understand if you actually want to do either, and if so, which.
If you're still set on applying elsewhere, try do it so that you have the LSE as a backup. As for how your single year of university would reflect on your profile, I'd say generally it's a good thing - because it's your chance to show them you can adapt well to the university workload (if you have good grades). I'm not sure to what extent would apply in this case as I'm not familiar with how much content overlaps between Law vs History/Eng Lit.
Do note you're definitely going to have emphasise your conviction behind why you want to switch, though.
Resits may not really affect your profile, especially if you get an A*, but you've to remember that people achieving similar grades to you first time will (generally) be preferred to my knowledge. Perhaps this is mitigated with people applying for Law (who have the LNAT to consider) such that someone who may be generally 'less preferred' with a resit, but then does amazingly well in the LNAT, could still be offered a place over someone who is sitting A-Levels the first-time but gives just an average LNAT score.
Hope this helps, just my 2 cents. Good luck with your decision!