What documentation is required for applying for the METV from London?

Recent reports indicate you need to show a flight to Thailand, a flight out of Thailand within 60 days of your arrival, and then one more flight back to Thailand. That should be 2 entries and enough to justify your application.

Usually a first week stay is just fine. If they do not like it they will e-mail you to follow-up and ask for additional information.

Do not take this "additional information" risk with your entries and exits though, or they will issue you a single entry visa and keep the amount you paid for the multiple entry. Provide the entry, exit, and entry on the initial application.