I asked a similar question last year. Basically pushchair was delayed coming back into Gatwick and BA couldn’t get it back to us before our next flight (back out of Gatwick on BA on a different booking).

BA refunded the £70 Argos pushchair I bought to tide us over no problem.

Edit:- It won’t help you this time, but I now follow this process when gate checking pushchair, as it seems staff are often a little unfamiliar with the correct process.

• Check receipt against tag, and take photo of tag.
• Clarify with gate staff where it should be left.
• Ask crew onboard to check on iPad it has been marked as Return To Door.
• On arrival try and clarify with a member of ground staff asap that it is coming back to the door.