Is the fitting of a video doorbell in a home used for business purposes covered by GDPR?

The short answer is “it depends”.

Here is a link to the ICO’s guidance for people using CCTV in a domestic setting https://ico.org.uk/your-data-matters/domestic-cctv-systems-guidance-for-people-using-cctv/.

The second paragraph on this page is the most important one to consider.

Here is a link to the ICO Checklist on the business use of CCTV https://ico.org.uk/for-organisations/data-protectionself-assessment/cctv-checklist/, you will need to consider this particularly if you have clients coming to your home.