Would I be likely to get into Cambridge for computer science?

Firstly, its always worth a try. If you get rejected then you still have 4 other uni offers to choose from (usually), and you can only pick two anyway. If you get in then great. You have nothing to lose by applying.
What I will say is that Cambridge are very famous, thus very popular and get a lot of applications. They can afford to choose only A*A*A*A* students because of their prestige, so bear in mind you will be competing against people who may have insane A Level grades.
All of that extra-curricular stuff will also play in your favour though, so make sure to big that up too in your personal statement.
Lastly, I recommend taking Further Maths fully, if you're doing it at all, as a university like Cambridge will probably look at an AS level as a missed opportunity. Further Maths involves a lot more work but bear in mind it also makes regular A Level maths easier because you learn more advanced stuff sooner.

My advice would be to apply if you want to go there, but know that you must go not just out of your way to show willing and determination, but beat everybody else at that game at the same time. You have to shine more than everybody else (and let me tell you, everybody else applying to cambridge WILL shine, a lot), and it may be quite difficult unless you plan on getting 3-4 full A* A Levels.

For reference, my friend applied to Cambridge having done A2 Further Maths, predicted A*A*A*A and he was rejected, though I'm sure each case is considered on its own merits

Good luck with whatever you choose,
The MIDI Man

GCSEs:
9 - Maths, Bio, Chem, Physics, Comp Sci & Spanish
8 - Business studies & Astronomy
7 - History
5 - English Language & English Literature

Currently my A-level predicted grades are at A* (Physics), A (Maths) and A (Computer Science) but these could change based on my mocks.

EDIT: My predicted grades are now A*A*A*

I've done some supercurricular stuff already and have some more to do over summer:
- Silver Award from the UKMT SMC
- Merit from the UK Bebras Challenge
- In the process of creating my submission for the BPhO Computational Challenge
- Working my way through a book about computer science
- Got a Nuffield Research Placement that's computer science related

I've also got a bunch of stuff I could put on my personal statement just from generally being a computer nerd like learning python and C++ and the basics of some other languages like C#, Javascript & Kotlin.

Apparently Cambridge place less emphasis on your GCSEs when deciding to give applicants interviews and I will be taking an IELTS test over the summer, however I'm still worried that my 5s in English will lead to my application getting rejected. Also Cambridge heavily recommend doing further maths in preparation for computer science at university although I am planning on taking AS further maths in my second year.

I'm still unsure whether to apply in the first place as I'll have to spend time revising for the TMUA that I could spend on other stuff like revising for the IELTS and having a later deadline could allow me to get more impressive SMC and Bebras results.

Hey man, were you able to submit your computational challenge work? I haven't received any instructions, and I've had no luck contacting the BPhO team. Thanks

Sorry but I haven't heard anything from the BPhO Comp Challenge team either and I definitely remember signing up on the online form. The last e-mail I got from them was back in June with a link to the registration page.

Sorry but I haven't heard anything from the BPhO Comp Challenge team either and I definitely remember signing up on the online form. The last e-mail I got from them was back in June with a link to the registration page.

Hey, I just got a response with submitting details from BPhO, so it seems all good now. Best of luck