I hear you... And am. Totally sorry for you.
Of course it's your fault but I can understand that you get angry and are very disappointed.
The way how you write here.. Criminal act.. Thieves.. Doesn't help you nor gets sympathy..
If you have talked like that to the check in agent it s pretty clear why that happened.
I had the same situation where me and my partner flew from prg to atl thru lhr.. Interesting thing was he got the online check in to lhr. And there we realized his esta was invalid.
BA was more than helpful and did everything possible... Meaning he could clear security 20min before departure.. What ba people on the forum here know is limes impossible at terminal 5.
So ba can be very helpful.