Tonden, 38, whose name at birth was David Alain, doused his head and clothes with petrol, and set himself on fire at the monastery on Thursday evening.
Monks and local police said they were unsure whether Tonden had been depressed and committed suicide or that it was a political statement, the Telegraph reports.
According to the paper, Tonden died on the day that the Chinese Communist Party enacted its once-in-a-decade leadership change, with Xi Jinping taking over from Hu Jintao.
In the past week alone, at least nine Tibetans were reported to have self-immolated in protest at what they say is religious and cultural repression by the Chinese authorities.
In all, 74 Tibetans have now set themselves on fire since 2009 demanding freedom and the return of the Dalai Lama, who has been in exile since 1959.
Tonden was keenly aware of the Dalai Lama's plight, having met the spiritual leader last year when he visited the monastery, the paper said.
He also met the Dalai Lama's sister in September when she came to Nalanda and its nearby meditation centre, Vajra Yogini, it added.
London: A 38-year-old British man has become the first Western Tibetan Buddhist monk to die by self-immolation at a monastery in southwestern France.
First Published: Saturday, November 17, 2012, 12:22