Peter Tatchell has urged the government to sever all ties with Brunei, as it introduces a law which allows LGBT people to be stoned to death if they engage in gay sex.
Appearing on the breakfast show, the human rights campaigner said the international community had "looked the other way" when news of the laws first emerged.
"This very harsh Sharia law didn't happen out of the blue. Two years ago the government of Brunei said they were going to introduce them," he said.
"The international community basically looked the other way, and so did our Royal Family."
A number of celebrities have been boycotting Brunei-owned hotels, including London's The Dorchester, but Mr Tatchell called for more action.
"Suspending diplomatic relations, threaten to suspend migration, we should suspend military ties," he suggested.
He continued to say that consumers could avoid holidaying in the country and not buy products from there, if they want to make an impact.
"We can decide no, we don't want to award governments and regimes that have poor human rights records, and that's another very powerful message."