In your “simple application” (and your main one) you should be handling this using the rate limit headers CH send (on the http responses) rather than just counting up to 600. You may well be doing this already of course! Some info in and linked from this thread:
Not from Companies House myself but if I recall they certainly do take IP address into consideration (including requests to both the API and website access). I can’t find the specific item on this that I remember but from a couple of years ago this thread has a response:
Slightly more recently there’s a note about the API and more general (AWS) limits:
Good luck!