The Alien Business Act foresees some exemptions. Some occupations do not require a Work Permit:

• Members of the diplomatic corps or consular missions, as well as their family and personal servants
• Representatives of member countries and officials of the United Nations and its specialised agencies, as well as their family and personal servants
• Persons who perform duties on missions in the Kingdom under an agreement between the government of Thailand and a foreign government or international organisation
• Persons who enter the Kingdom for the performance of any duty or mission for the benefit of education, culture, arts, or sports
• Persons who have been received special permission from the Thai government

THis comes under article 3 or 4 or 5 so may I ask what you reference to there is no provision is.

As said above,

Please share a link or proof that a work permit exemption letter has EVER been issued by the Labor Ministry for 3 or 4 or 5.... or 1 or 2 for that matter.

If you're that interested why don't you write directly to the British Council and ask them to explain how they ensure that their staff work legally?

No letter would be needed as there is no need for a work permit..