Unconventional UCAS Points Distribution

I am currently in year 12, and attend a very small school - 14 pupils in sixth form! Due to a lack of the subjects I wanted being offered, and illness on my part I have ended up doing the following

AS English: predicted grade A (97.5% in coursework, no exam results yet)
AS Human Biology: predicted grade A
A2 Human Biology: Predicted grade overall A*

As you can see I have taken a whole A level in one year. Next year I plan to study A2 English, and the full History A level, AS & A2 alongside AS Creative writing (coursework completed but not entered - grade A)

This will give me 3 full A levels and 1 additional AS

The problem is I wish to study law at Cambridge, or another good University, which I realise is ambitious. I am worried since I will be applying via UCAS with 1 full A level and 1 AS level instead of 3/4 AS levels as is standard.

The school is happy to write and explain the situation.
I also have been diagnosed with clinical depression and Aspergers syndrome four years ago, and the nhs is willing to write an explanatory letter on how this has affected my studies at both GCSE and A level, (I did my GCSEs in 1 year due to depression making it impossible to attend school. I only 7, but I did do Maths, Triple Science, English Language and Literature and History all grade A*)

It would be really helpful if anyone would know whether Cambridge is still an option, and if I can enter via UCAS with the qualifications I will have...

You may want to consider studying Law at A Level if you wish to apply to a top university like cambridge for it. I won't pretend to be an expert on the subject but I'm pretty certain if you take the subject you wanna take on to HE at A level it will increase your chances.

Applicants are not required to have studied Law at GCSE or A Level. Those who have done so tend not to have any special advantage once they begin studying Law at university. Academic subjects other than Law will generally provide a solid foundation for the course, as well as giving a desirable breadth of experience.