Well I've spoken to you a few times and I'm applying to Optometry so I have already researched stuff without giving my opinion blindly. So I can say with full confidence that you made the right choice assuming you've always wanted to go into Optometry. The optometry course is similiar across all 8 UK uni's that do Optometry as you know and the employment rate is similiar for all (80%-100% thereabouts) so it's not like you have disadvantaged yourself by going to Anglia Ruskin for Optometry to become an Optometrist.
But you know, the ignorant people who know nothing about the course and just look at what uni you go will say "you're gonna struggle later on" and blah blah when it's far from the truth providing you do well in the course and knowing that Optometry-related jobs aren't that hard to get after graduating.
Math is seen as a good field to study. It's rigorous, and it can lead to good salary after graduation (what I would consider a good career). Similarly, LSE is seen as a very good place to study.
On the other hand, optometry is not generally regarded as being a particularly prestigious field to enter - particularly because it's commonly assumed that anyone with the ability to do so would prefer an education as an ophthalmologist instead. And compared to LSE, Anglia Ruskin is not widely regarded as a prestigious or top-class university.
I think that the bad choice was made when you applied to LSE; it's no fun house.
Why did you apply at LSE if you wanted to do optometry, you just prevented someone who wanted to do it surely?
It depends what you want to do. The two degrees strike me as very different.
Optometry is primarily a practical subject and involves a lot of interaction with members of the public. There is a clear career path to follow once you qualify.
I know much less about stats etc - but I'd assume the degree would be much less fun, no hands-on element, and whatever job you did at the end of it would be likely to involve more of the same. The earning prospects would be higher for this latter degree - but I can't even imagine wanting to do it, whereas optometry would be quite interesting.
If you're a people person, and like practical skills, you've probably made the right choice for you. If you want to move towards ophthalmic work rather than optometry, there are opportunites to do clinics in hospital etc to learn a bit about it. You'd have to do a medical degree to actually become an ophthalmologist though (eg after your optometry degree. I know 3 people who've successfully done this .