The Archbishop of York has asked the Government to raise with China the recognition of the Dalai Lama as a religious leader.
In a debate in the House of Lords on Tibet, Dr John Sentamu noted that the Dalai Lama was not only a spiritual and religious leader for the people of Tibet, but recognised the world over.
"Will the Government nevertheless impress upon the Chinese Government that they should recognise and respect the Dalai Lama as a religious leader and not as a political leader?
"If they did that, it is possible that they would then have a dialogue," he said.
A similar suggestion was made by Lord Steel of Aikwood, who said that dialogue between the Chinese authorities and the Dalai Lama as a spiritual leader could bring an end to dozens of self-immolations by pro-Tibet protesters.
Baroness Warsi, Senior Minister of State at the Foreign & Commonwealth Office, said the UK Government was "deeply concerned" about the high number of self-immolations in Tibet and that its concerns were being raised "regularly" with the Chinese authorities.
She said Tibet had been discussed in the last round of the annual UK-China human rights dialogue in January 2012, although she was unable to confirm whether the Government had raised the suggestion of China recognising the Dalai Lama as a religious leader.
Baroness Warsi said the UK Government was concerned about the "lack of meaningful dialogue" with Tibet to address the underlying grievances in a "clearly worsening situation".
"We continue to encourage all parties to work for a resumption of substantive dialogue as a means to address the Tibetan concerns and to relieve tensions," she said.
"Of course, we continue to make the case to China that any economic progress can be sustained only if there is social progress as well."