It took about 2 weeks. However I had a family member in the UK send it to the Legalisation Office for me, and then the Embassy sent the final legalised document back to my family member.
Unfortunately not. The Thai Embassy in London needs to certify the UK Legalisation Office's stamp. Only the UK can certify that it's a legal UK document.
Presumably you were married in the UK? If so, this is why the UK Marriage certificate needs to be legalised by the UK Legalisation Office in Milton Keynes, then certified by the Thai Embassy in London.
Your employer should help you. They will need you to have a bank account so they can pay your salary. Someone from HR should be available to help you and they have a preferred bank and branch.