Paging through a result set is sometimes returning a String instead of Int for the start_index field. Besides being silly, this can break client code that relies on a cast to Int there.
This request produces an Int:
...
"start_index": 0,
...
This request produces a String:
...
"start_index": "50",
...
Agreed - and since start_index starts from zero looks like you’ve found the equivalent of a stack overflow… 
I think there are still outstanding bugs in the opposite direction e.g. when items_per_page and start_index are very small - see this thread:
https://forum.aws.chdev.org/t/is-there-a-bug-using-start-index-parameter/3079/2
If you wave at one of the Companies House folks (use “@” with one of their usernames) that might attract their attention faster - not sure?
Good luck