A long and expensive way out could be as follows:
[1] Santiago in Chile;
[2] Trans-Pacific flight from there to Sydney, Australia;
[3] Another long flight to Singapore;
[4] Flight from Singapore to Dubai;
[5] Flight from Dubai to Heathrow (on a nice comfy Emirates A380 with lots of leg room).
Doing it this way would probably blow a £3K hole in your wallet, and involve you in a logistical and bureaucratic nightmare,
but if you're able to bypass the USA this way, at least it'll get you home.
The problematic bit might be Australia, which tends to be a bit strict about bringing unwanted micro-organisms with you, but I suspect if you're not intending to
stop in Australia, you might be able to get around this.
The other way out is to find your nearest British Embassy, and see if they can dig you out of the hole.
This webpage might be the first step in digging you out of that hole.