Oh. You might need a transit Visa if they cannot check stuff through. India can be tricky for this stuff. I think the guys at BA may be right. https://www.indiaodysseytours.com/knows/india-transit-visa.html
The third condition seems be the issue here.
Sorry to hear about this. Good luck
Edit, appears Sri Lankan has no interline agreement with BA.
https://www.srilankan.com/en_uk/coporate/faq-details?type=11