Mogra was born in 1965 into a family of Gujarati Indian origin and emigrated to the UK at the age of 18 to study and settle. He was educated at Darul Uloom Bury, Holcombe, Greater Manchester; Al-Azhar University, Cairo; and the School of Oriental and African Studies, London. He is the founder and Principal of Khazinatul-`Ilm, Madaris of Arabic and Muslim Life Studies, in Leicester.
In 2000, he contributed to BBC Radio 2's Faith in The Nation examination of the afterlife amongst the main religious faiths. He has been a panelist on The Big Questions, a faith and ethics television programme broadcast live on BBC One.
Mogra believes that for British Muslims "our loyalty to Britain must be unquestionable".
Mogra has been a representative for Jewish-Muslim relations appreciating the similarities of communities governed by a code of law and ethics (Torah and Qur'an) and religious festivals and holy days. Asked to choose a favourite film for The Clerics' Choice in The Daily Telegraph, Mogra picked The Message, "you see through the eyes of the camera, as the Messenger would have seen it".
On 7 April 2013, Mogra took part in an interview on BBC Radio 4, condemning the men at the centre of the Rochdale sex trafficking scandal. He said that sexual grooming of non-Muslim girls by Muslim gangs was an abhorrent behaviour that was unacceptable regardless of race or religion. He expressed that as some of the perpetrators happened to be from a Muslim background, it was the duty of the entire Muslim community to condemn their actions. However he also cautioned that the paedophile scandal should be seen purely as criminal behaviour, warning that using labels of race and religion could "drive the problem deeper underground". Mogra also said that the Muslim Council was also working with different groups such as the National Society for the Prevention of Cruelty to Children, police and other Muslim groups to speak out against such crimes and assist in tackling the problem.
In 2016, he was awarded the Hubert Walter Award for Reconciliation and Interfaith Cooperation by the Archbishop of Canterbury "for his sustained contribution to understanding between the Abrahamic faiths".
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