Bangladesh Premier Sheikh Hasina was accorded a warm welcome upon her arrival at the Government House, the Thai premier's office
Sylhet is home to 40,000 British residents and where most of Britain's 500,000 Bangladeshi heritage citizens have their roots.
"The UK's ties to Bangladesh are nowhere stronger than in Sylhet Division,” Blake said in a statement after capping three days of her visit.
During the visit that ended on Wednesday, Blake met local MPs, Sylhet mayor, senior government officials and business leaders.
"I was delighted to get to see Sylhet and to meet its communities and people from Tamabil to Srimongol," she said.
Blake also hosted an Iftar reception.
"I was overwhelmed by the warmth and generosity of the welcome and by the determination of everyone I met to develop this region and work for the betterment of all who live here."