My wife recently flew from Xiamen to London on a combination of tickets (both tickets were purchased individually from the respective airline websites):
Ticket 1: XMN to AMS (Xiamen Airlines)
Ticket 2: AMS to LHR (British Airways)

Whilst checking in for her flight in XMN, Xiamen Airlines agreed to check the luggage all the way to LHR (on her luggage receipt it shows the same British Airways flight she was taking), so that she would not need to go through immigration in AMS and could just use flight connections. There was no delay of her first flight and there was a four hour connection time in AMS. Upon arriving in LHR her luggage wasn't in arrivals and it become apparent that her luggage was never loaded onto the BA flight. She eventually got her luggage delivered to the hotel 3 days later but since we don't live in London she had to purchase essentials to cover those days.

Theoretically which airline does she need to pursue for the cost of the essentials she purchased?