There is also a Vueling flight from AMS-LTN tomorrow at 7am. If that's on time, you'd be able to taxi from LTN to LHR to catch your original flight.
Might it be worth a quick call tonight to the US call centre to see if they could rebook you on that flight? It has an IB codeshare, although unfortunately not a BA one.
[Edit: Actually I think that LTN-LHR connection is a tad short of MCT, so it will be a no.]
Last edited by Ldnn1; Aug 11, 2018 at 3:17 pm