As someone who has lived in both cities, Bristol isn't that much cheaper than London. Ok, there is a difference in rent, but it's not as much as some would have you believe. Cost of renting has gone up since there was an exodus of renters from London during Covid. I lived in Bristol from the age of 17-19 and it is an exceptionally good place to be a student. The city has a definite identity and an openness toward progressive discussion and creativity, culminating in a really vibrant music and arts scene. Most of my friends went to London universities (inc. LSE) and they bemoan the lack of student experience offered by the universities and the cities' prohibitively expensive events circuit. Almost universally (whether it be LSE, UCL or Kings), they comment on the London uni environment being competitive rather than supportive. I would suggest there may be some truth that the more competitive universities require heavier reading, stringent concept-analysis and revision whereas Bristol/Manchester/Edinburgh etc would employ a more interactive approach.I was at one of the Bristol offer hold events recently and I think Bristol probably excels in developing a student-focused, discussion-based teaching environment. The facilities are new and the universities commitment to the department felt genuine and tangible. Important to note that you can do a year abroad (rather than just a semester as you suggested) although the course title is History BA with Study Abroad, rather than just History BA. It seemed that other prospective students hadn't made this distinction and applicants were advised to contact admissions to change courses.Having said all that, much of my research has led me to the conclusion that LSE is the most 'prestigious' choice for History outside of Oxbridge and its continuation statistics are fantastic. There would undoubtedly be a higher proportion of international students too which I feel is a major positive factor considering the nature of the subject. Ultimately, if you want a mix of good university and great student experience then Bristol should be considered, but if you are deciding purely on academic merit then LSE appears superior.