1. What is the process?

2. Can an emergency document be issued quickly and will Thai immigration except it for use of a visa extension while waiting for a new passport?

Thank you in advance 

Moved to the Visas and Migration to Other Countries forum. It's the weekend, so you will receive a faster response in that forum.

The UK emergency travel document is not a passport and AFAIK Thai Immigration won't put any extension stamps in it. It's solely a document to facilitate your return home.

 

Due to the UK passport office staff working mostly from home and a surge in summer holiday passport applications and renewals domestically,  the turnaround time to Thailand for a routine passport replacement has been recently reported as between three and four weeks. Not sure if replacing a lost passport introduces any further delays.

 

Either way, the first step is to get a police report of the loss.

Yep, first step police report.  Get it translated into English.  And get the application started as soon as possible.  I replaced a stolen passport a few years back and the application took no longer than it would have for a normal replacement.  I got the translation done by some visa office in Pattaya, no need for any certification.

You can report a lost or stolen U.K. passport online and there is no requirement to obtain a police report.

You receive an online confirmation of the cancellation

https://www.gov.uk/report-a-lost-or-stolen-passport

6 minutes ago, ab1594 said:

https://www.gov.uk/report-a-lost-or-stolen-passport

A good step.

report it as lost at the police station and get a report number.

The UK office for handling passports is in the Trendy building upper floor level, I think Soi 13 off Sukhumvit?

check if they have an info website for what you need to do.

21 hours ago, johninbkk71 said:

2. Can an emergency document be issued quickly and will Thai immigration except it for use of a visa extension while waiting for a new passport?

Quote

What an emergency travel document lets you do

You can use an emergency travel document to travel to your destination through a maximum of 5 countries. You can also normally use it to return to the country you’re applying from if you live there.

Your travel plans (countries and dates) will be printed on your emergency travel document. If you change your travel plans once you have your emergency travel document, you’ll need to apply for a new one.

Get an emergency travel document

(the short answer to your question is YES)

HTH

29 minutes ago, evadgib said:

Get an emergency travel document

(the short answer to your question is YES)

HTH

The Embassy made it clear (in the context of the recent-ish VFS office closures) that emergency travel documents would only be issued to those who had made specific plans for travelling back to the UK. If the OP is a long-stay non-immigrant there is no way in which he could obtain one solely for the purpose of applying for an annual Immigration extension of stay for retirement, marriage, etc.