Does duty of care extend to the cost of obtaining a eta/visa/e-visa where there is a misconnect in a 3rd party country which requires you pay an immigration fee to enter and avail yourself of overnight accommodation which BA have advised you to arrange?

The specifics are - flight Lusaka LUN - Nairobi NBO - London LHR, single BA ticket, both flights BA marketed although the LUN-NBO flight is Kenya Airways operated. If all had gone to plan the connection would have been airside at NBO so no Kenya ETA required.

The late operation of the LUN -NBO flight resulted in a missed connection to the BA service to LHR. Rebooked onto the next available service which was the following day. BA indicated I should book a overnight hotel at NBO myself and seek reimbursement. NBO has no airside transit hotel so only option is to enter Kenya which requires at expedited transit ETA fee. This fee is directly incurred due to the missed connection and is the only way to obtain overnight accommodation.

I will add the transit visa cost to my claim to BA and see what they say but wondered if anyone had previous success or failure with claiming this sort of cost.