We are looking to develop a cloud based application which will use the Companies House API to perform backend validation; the backend services will be assigned dynamic IPs that may change if/when backend services scale/fail which is standard practise for cloud backend services.
Is there anyway to authorise such a service with the Companies House API ?
Just register for an API key, and use that. No other authentication is necessary.
The optional IP address restriction that you can complete when registering for an API key is purely for you to lock down JavaScript access to a particular machine (or machines). This is because your API key will be visible in the javascript on that client. It is up to you whether you need to invoke this protection or not.
The optional Domain name restriction is again for Javascript access, and is necessary to avoid CORS access issues. Assuming a web based solution, set the domains here that your web application is served from - the browser will do the rest.