Gillian Gibbons, 54, was arrested on Sunday on blasphemy charges in Khartoum, the capital of Sudan, after her class of primary school pupils named the soft toy in September.
Islamic Sharia law is in force in some parts of Sudan, including the capital.
"The Sudanese legal system has to take its course but common sense has to prevail. It's not about disrespect for Sudan, it's about being absolutely clear that this is an innocent misunderstanding," David Miliband said.
Although Gibbons has said that the act was not intended in any way as an insult to the Prophet Muhammad, she has been charged with insulting religion, inciting hatred and showing contempt for religious beliefs. If found guilty she could face up to 40 lashes, six months in prison or a fine.
Sudan is 75% Muslim, and Muhammad is a popular name in the country. A boy from Gibbons' class stated on Wednesday that he had thought of the name himself, and other pupils and parents have urged leniency.
However, hard-line Muslim clerics have rejected Britain's claims that the incident was the result of an "innocent misunderstanding."
"What has happened was not haphazard or carried out of ignorance, but rather a calculated action and another ring in the circles of plotting against Islam," the Sudanese Assembly of the Ulemas said in a statement.
"It is part of the campaign of the so-called war against terrorism and the intense media campaign against Islam," the statement concluded.
The incident is the latest in a series of international clashes involving so-called Western values and Islam. Last year, caricatures of the Prophet Muhammad in some European newspapers sparked riots in several Muslim countries.
Gibbons has since been sacked by the Unity High School, the private English-language school where the incident took place.
