Joshi is a senior member of the Bharatiya Janata Party (BJP), of which he was the President between 1991 and 1993, and the former Member of Parliament for the Kanpur parliamentary constituency. He came in contact with the RSS in Delhi at a young age and participated in the Cow Protection Movement in 1953–54.
During the 1992 Babri Masjid demolition, Joshi played a very prominent role. He along with other BJP leaders like Lal Krishna Advani, Uma Bharti, and Kalyan Singh, were among those who were behind the nationwide Hindu nationalist movement to demolish the mosque. Lakhs of karsevaks had gathered at the site from across the country. The incident triggered communal riots nationwide.
On April 19, 2017, the Supreme court ordered a day-to-day trial in the case and said it should be concluded within two years. The court also restored criminal conspiracy charges against Joshi, Advani, Vinay Katiyar, Sadhvi Ritambhara, and Vishnu Hari Dalmia.
In November 2019, while passing its judgment on the related Ayodhya title dispute, the Supreme Court said that the 1992 “destruction of the mosque and the obliteration of the Islamic structure” was an “egregious violation of the rule of law.”
In 2020, six years after Narendra Modi came to power, the special CBI court acquitted all 32 accused in the Babri Masjid demolition case, saying there was insufficient evidence to prove criminal conspiracy in the case.
Immediately afterward, Surendra Yadav, a retired Judge who had passed the acquittal order, was made Deputy Lokayukta (III) in Uttar Pradesh.