AS Grades, Economics and Uni Application questions...

So I recently got my AS level results:
A in Chemistry (275/300) AS
A in Physics (277/300) AS
A in Economics (187/200) AS
A in Mathematics (539/600) A - Level

With those results, I would be dropping Chemistry and taking Further Mathematics, Physics and Economics to A-Level (and retaking one exam to get an A* in Mathematics).

The universities I am looking to apply were mainly LSE and UCL and I am planning to apply for Economics at those universities. However, both universities demand an A* in Mathematics at A - level. I did my course early, I only achieved an A. Does this mean that when I apply, I will be rejected by UCL and LSE since I received an A (instead of an A*) already or will they assume I will be retaking to get an A* and give me a conditional offer? How does this work out? Are my chances reduced?

Also, would it be a good idea to apply to Cambridge as well? The average UMS I achieved was 92% - 94% except with an average of 89% in Mathematics. This means that I will have to retake one exam in Maths (C4) to get an A*.
Could someone let me know or provide some information (apologies for any silly questions asked in advance).

Regarding LSE and UCL you may have to email them about that, it's not as if your retake will be delaying your application so I don't see why there would be a problem

Your UMS are pretty high so you should be okay at Cambridge, just make sure your interview and PS are good!

If you are planning on applying to LSE may I direct you to the stalking page (http://www.thestudentroom.co.uk/showthread.php?t=3510999). It would be really useful if you could fill it in

Well done on your results!

Thanks. So I'll email LSE and UCL then to make sure. But they wont reject the application straight away right? I mean, they are assuming I will be retaking to get the A* or would I have to tell them and if so, how?

And also, I will be taking a STEP paper in Mathematics, so would I have to notify them about this (since it is favourable to my application to do a STEP paper).

I'll have a look at that stalking page in a bit as well.

Thanks