The 72-year-old monk -- widely respected in the West and courted by celebrities but accused by Beijing of fomenting trouble against Chinese rule in Tibet -- arrived in Britain on Tuesday on the second leg of a five-country tour.
One Shugden follower, Kelsang Pama, said Prime Minister Gordon Brown, lawmakers and Western media were mistaken in portraying the 1989 Nobel Peace Prize winner as a champion of human rights.
Instead she said that he sanctioned the outlawing of their worship of the deity Dorje Shugden "for no valid reason" and the expulsion of practitioners from monasteries, and that he forced Tibetans into abandoning support for the movement.
"He comes to the West, talks about religious freedom, love and equanimity but then his actions are not following his speech," she said. "Why do we accept this from this person when any other leader in this world is questioned?"
In particular, she said it was now not clear when the Dalai Lama was speaking as a religious or a political leader.
Pama, also known as Helen Gradwell, said his actions were affecting Buddhist monasteries particularly in India as well as inside Tibet.
Indian police have suspected Shugden supporters of involvement in threats to the Dalai Lama and even the murder of a respected Tibetan scholar and two of his followers.
But Pama insisted they were a peaceful movement and "not against the Dalai Lama," also rejecting other claims that they have the tacit support of the Chinese government.
Instead she said they were trying to secure talks with the Dalai Lama or his representatives over a theological dispute.
"The moment the Dalai Lama will start a meaningful discussion we will stop our demonstrations," she added.
Tsering Tashi, the Dalai Lama's representative in London, told AFP later that they respected the Shugden Buddhists' right to protest but said their allegations were untrue.
"It (their worship of Dorje Shugden) goes against the very concept of the teachings of the Buddha. It degenerates Buddhism into a spirit worship," he added.
The group had not made any formal request to meet the Dalai Lama or his representatives, he added.
