Mr Burke and his business partner opened the area’s first LGBTQ+ pub, The Rising SE1, in April last year.
He told the meeting: “We are currently the only LGBTQ+ pub in SE1 and this to our knowledge will be the only LGBTQ+ cinema in all of London.
“This licence will allow us to operate a safe space for all in one of the most LGBTQ+ densely-populated areas of the country.”
Mr Burke said the cinema would double the number of LGBTQ+ venues in the area.
The licensing committee gave the new cinema and bar permission to open until 23:00 Sunday to Wednesday and until midnight from Thursday to Saturday.