Hey, when you submit your UCAS there's nowhere where you really can say, "I didnt take further maths", because this raises questions like, why? - leading to you saying you only got a 7 in maths. For LSE BSc econ, this is the info:
Further Mathematics at A-level is also desirable, and is acceptable for entry in combination with Mathematics and one other A-level. In these cases we'd prefer that the third A-level should be an essay-based subject. If you take four or more full A-levels, you’ll be expected to achieve A* A A (with A* in Mathematics), and a pass in the fourth A-level. We understand that not all schools/colleges offer Further Mathematics and you won’t be disadvantaged as a result – please could you and/or your referees indicate this on your application form.
For finance:
Further Mathematics at A-level is also desirable – and accepted with Mathematics and one other A-level. We understand that Further Mathematics is not available in all schools/colleges – you will not be disadvantaged if this is the case. Please could you/your referees indicate this on your application form.
Here, they are saying that, if your school offers FM you ought to have taken it, however, since you havent taken it, that is perfectly fine, as long as you achieve an A* in Maths (predicted is what will be sent to UCAS so dont slack off in Y12), however your school doesn't need to mention that you were unable to take FM, due to their guidance, as this will not reflect well on you.
My advice, DON't mention further maths in your PS or reference, but DO mention, the fact that you achieve highly in maths, and try to engage outside of school in maths, to show that you are academically extending yourself beyond the curriculum, and have your referee mention this in your reference.
So in answer to your actual question, no you shouldnt indicate that you couldn't take FM, especially since LSE is a highly competitive university that is likely to look at GCSE grades, when comparing their applicants, all of whom are bound to be very similar.