Excellent question. The short answer is: It depends entirely on your nationality, your final destination, and whether you need to pass through UK border control (enter the UK).
British Airways is just the airline; the requirement is set by the UK government’s immigration rules.
Here’s a breakdown to help you determine if you need a transit visa:
You need this if you are from a specific list of countries (e.g., India, Pakistan, Ghana, Nigeria, many others) and you will be transiting airside in the UK on your way to another country.
You do NOT need a DATV if: You have a valid visa for the USA, Canada, Australia, New Zealand, or an EU/EEA country, and are traveling to that country. You have a valid permanent residence permit for one of those countries. You hold an EU/EEA family permit. You have a valid UK visa for any purpose.
You must apply for this visa if: You are from a