My passport is currently with UK passport office being renewed, and I urgently need to travel to the UK. I have been issued an emergency travel document which allows me to enter the UK, and they will not return it at border control, so it is only valid for one one-way trip. I understand I can re-enter the US with my green card alone, but will I be able to leave the UK without my British passport? I have called the US embassy (no help at all), the airline said it was not up to them and to check with the respective government agencies, but I cannot seem to get a straight answer!
As far as the US government is concerned, a green card holder does not need a passport to enter the US. See this CBP answer:
United States (U.S.) LPRs do not need a passport to enter the U.S. as per 8 CFR 211.1(a)
The US government allows airlines to board green card holders for travel to the US without a passport. See the CBP carrier information guide, page 28:
A Lawful Permanent Resident may travel to the United States without a passport with a Permanent Resident Card (Form I-551).
Since the UK does not have physical exit immigration checks for departing passengers, the only people who will stop you from traveling to the US is the airline. Just because the airline is allowed to let you board you without a passport, doesn't mean they have to let you board without a passport. So asking the airline is the right thing to do.
I don't know why the airline didn't give you a straight answer when you asked them. Perhaps you are phrasing the question wrong. Rather than asking whether you will be able to leave the UK or enter the US (which sound like things to do with the immigration agencies), you should specifically be asking whether the airline will allow you to board the international flight to the US without a passport.
Another possibility I haven't mentioned is that perhaps the UK has regulations on airlines to require departing passengers to have passports. Maybe someone can check whether this is the case.
Yes, you can 100% enter the US on your green card. The handling agent should coonsult TIMATIC, putting UK as the nationality and US as residence, whereby the "Permanent resident card" will appear as a "Passport exemption".
What route is it you're planning to fly? Then I can tell you what handling agent in the UK to contact, as they'll be the ones to board you.
UPDATE: bring a printout of the email you got from GGS, just in case.
I have done this before.
It can be a real hassle, but it is doable.
Leaving the UK, I had to be patient, but insistent with the check-in agent. I had to wait for a supervisor of some sort to come and confirm that I could board.
Arriving in the US, you may have similar issues. I had not trouble at the time, but this spring I had an immigration officer request my passport after I handed him my green card.
Give yourself a tonne of extra time in the UK and be prepared to stand around for a long time. The law is on your side, just keep patient, be very polite and assert your rights.