@jimYour assumption is correct - there is nothing in the documentation that restricts commercial use.
You will find the T&C of use of the Companies House API here:
The guidelines can be summarised as follows:
API rate limits - You can make up to 600 requests within a 5 minute period.
API key security:
- Do not embed API keys in your code
- Do not store API keys in your source tree
- Restrict API key use by IP address and domain
- Regenerate your API keys
- Delete API keys when no longer required
If you use the API to generate income as part of a business, you will need to register the business with either Companies House or HMRC depending on the nature of ownership of your business: Set up a business - GOV.UK
If you wish to run your business as a limited company or LLP, you will need to register with Companies House.
However if you wish to operate as a sole trader or a traditional partnership, you will need to register for self assessment with HMRC. Register for Self Assessment: Register if you’re self-employed - GOV.UK