The US won't approve anything without an open skies deal on their terms with the UK. Their terms consist of the right for any American carriers to fly into any UK airport at will, with the take off and landing slots provided by the incumbent (British) carriers. It also calls for unrestricted fifth freedom rights from the UK for US carriers. In return the British aviation industry will receive:
1) Less slots at our home airports.
2) Unrestricted access for US carriers to LHR, sparking a destructive trans-atlantic price war which only the heavily state-subsidised US carriers can win.
3) Er..........thats about it.
I wouldn't hold your breath for an agreement.