Will sociology affect my chances?

It's fine. You need maths and FM for maths degrees, and you have that.

However that said, it's not generally advisable or practical to apply to two separate degree programmes - you only get one personal statement to go to all unis.

If you are interested in two subjects you should aim to apply to a joint honours. That said, it's worth bearing in mind economics at degree level, especially at unis like LSE, is inherently very mathematical in much the style of A-level Maths. It's not really that similar to A-level Economics by all accounts.

Maths at degree level (including in joint honours courses) by contrast is very different to A-level Maths and FM. Enjoying A-level Maths/FM and doing well in them does not necessarily imply you will like the nature of maths at degree level (or indeed do well in it).

In any event your subject combination is fine for either or a joint honours in both, but I would recommend you do some wider reading in the maths area looking at actual material you would be studying in first year of a maths degree (e.g. real analysis, some introductory abstract algebra, abstract formulations of linear algebra etc). This will give you a better idea of the type of maths that often makes up a large part of maths degrees - namely very abstract, very proof based, and with much less of the "problem solving" type maths from A-level.