I think I am correct. You are allowed a large number of days layover in London, coming or going to your next destination (Paris). Yes, you need to call BA to do this and sometimes they charge for the service and sometimes they realize you can’t do it online and the wave the fee. It is useful to go online and identify the flights you want, see if there are reward seats available, and note them so you can tell customer service what you want. Finally there is a significant departure tax built into your 241 ticket. Your flights to and from Paris most likely require a plane change in London.
Last Oct, we flew Club World Dulles to London to Jordan, then Egypt to London, stayed in London about 10 days, and returned to Dulles. Taxes and fees were about $1200 total for business class.