Hey there, I did IB and not A-Level, but was choosing between the same choices some time ago. I also applied to LSE and Warwick for courses other than straight econ, and did not apply to Manchester nor Bath, so don't know much about these two. LSE is a great choice for either straight econ or econ combined with something else, but count on it being highly competitive. I applied for Maths and Economics at LSE with 45/45 predicted IB points and a solid TMUA score and wasn't given an offer because my personal statement "didn't convince them that I was equally interested in both parts of the course", which surprised me because I put in a lot of effort into trying to make my ps suitable for both straight economics (because that was the only option for Cambridge) and Econ with Maths/Stats in my other options.
As for pure econ vs econ and maths, if you're a highly technical person who enjoys maths a lot (like me) and imagine yourself working in a quantitative field/position at some point, I'd probably go for Econ and Maths. It will be a better fit for many positions, from being an analyst or actuary, to nearby fields like statistics or data science. In my experience maths is valued a lot for being rigorous and demanding, so might have a bit more value than pure economics. Also keep in mind that the maths you will do in a Econ and Maths degree will likely be closely related to social sciences and economics, at least that's what LSE writes on their pages. So it's not like you're doing both a pure econ degree and pure maths simultaneously, more like doing econ but the more quantitative side of it (as I understand it). That being said, if you mostly enjoy writing essays, reasoning and exploring different sides of an argument, then pure econ might be a better fit. It will still include a lot of mathematics (no getting around that in most courses), but will be a little more versatile than Econ and Maths. I.e. choosing Econ and Maths narrows down your scope compared to just econ, it's more specialised. This means pure econ it keeps your options open a bit more, but might also make it harder to access the more quantitative positions like the ones I mentioned.
In the end I recommend looking at the breakdowns of the course components/modules for each of your options and seeing which one you'd enjoy more. I'd prioritise that above your career opportunities etc, as those will be very good with both degrees. I do recommend choosing one though and applying for the same (or very similar) courses in all your unis, since as I said I tried to balance my ps between close but non-identical courses and it didn't turn out the best.
Let me know if you have any more questions.